The lengths of lines are easier to guess than angles. Also, that year 11s will be more accurate at estimating. Essay Example

The lengths of lines are easier to guess than angles. Also, that year 11s will be more accurate at estimating. Essay Example The lengths of lines are easier to guess than angles. Also, that year 11s will be more accurate at estimating. Essay The lengths of lines are easier to guess than angles. Also, that year 11s will be more accurate at estimating. Essay In this investigation, 3 year groups years 9, 10 and 11, were asked to estimate the lengths of some lines and angles, and the results that the pupils produced are going to be analysed to try and prove or disprove the hypothesis of:The lengths of lines are easier to guess than angles. Also, that year 11s will be more accurate at estimating.The reasons I think these things are because people are more used to seeing lines than they are angles, so this could mean that they are better at estimating the length of lines. The reason I think they year 11s will be more accurate is because they have done maths longer than the year 9s, so they have had more experience.I will be using an example of one line, and one angle, and the results of Year 9 and Year 11 estimates. This is secondary data which has been previously recorded, during a survey to find out the estimates that the pupils gave. This data is continuous as it is As there are 117 year 9s and 145 year 11s I will have to reduce the size of my sample as these numbers are too large to handle, so I will be using a stratified method to reduce the size of the samples as this method keeps the results for the year groups in proportion to each other.I am going to be sampling 60 people in total, out of the year 9s and year 11s, as this is a manageable amount, and it can represent the data from the two year groups accurately as a smaller number might not show the difference in results suitably.To choose my samples I am first going to add together the two total numbers of each year group, which is:145 + 117 = 262 (Year 11 / Year 9)Then I am going to do some calculations. For the year 11s I am going to do:(145 / 262) x 100 = 55.355.3 is about 55 %This means I need to have 55% of the sample of 60 from year 11s results. 55% of 60 is 33, so I need 33 samples to be Year 11 samples.For The Year 9s I am going to do:(117 / 262) x 100 = 44.644.6 is about 45%This means that 45% of the sample of 60 need to be Year 9 results. 45% of 60 is 27, so I need 27 Year 9 samples, which gives you the total of 60 samples.To get these 60 samples from the 262 results I am going to use a random systematic method. To do this I will use a random number generator to find a number from the year 11 and year 9 data, and I am then going to count down from that number, and every 7th piece of data I am going to use. (As 7 was the number that came up when I used a random number generator to find a number between 0 and 10.)Year 9 Random Number Generator91 was the number the generator produced for the year 9s, so I am going to use the 91st piece of data, and then every 7th piece of data after that I am going to use until I have my 27 pieces of data. So, the numbers I am going to use are:91, 98, 106, 113, 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94, 101, 108, 115, 5, 12, 19, 26, 33, 40Year 11 Random Number Generator127 was the number the generator produced, so I am going to start from the 127th piece of data and count down 6 piece s of data (as 6 was the number produced from the generator between 0 and 10) and then every 6th piece of data after that I am going to use until I have the 33 pieces of data I need for the year 11s. So the pieces of data are:127, 133, 139, 145, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 5, 11, 17, 23, 29Once I have collected my samples, I am going to draw some grouped frequency tables, which will also have frequency density on. These tables are there so that I can find the mean from grouped data. Also, because the data is put into groups it is easier to handle. I will also find out the spread of the data from the mean using standard deviation.Then, I am going to draw some histograms, using the frequency density from the grouped frequency tables. These will show the density of the data in certain groups. This shows which group had the most estimates in it.Next, I am going to draw some cumulative frequency tables and curves. These will show the inter-quartile range. This shows the range of the quartiles. Also, from the cumulative frequency curves I can draw some box plots. These will show the inter-quartile range, median and lower and upper quartiles in a more compact and easy to read way.Then, I am going to draw some percentage error tables. These will show the error of the estimates and if people estimated below or above the actual size or length of the line.I am then going to draw some scatter graphs showing the errors from the percentage error tables. From these you will be able to see if some guessed below the actual length of the line, and whether or not they guessed below the size of angle as well.Then I am going to draw stem and leaf diagrams for each year group. From these I will be able to find the median and mode. Stem and leaf diagrams show all the data in an easy to read way.Finally, I am going to find The Spearmans Coefficient of rank. This shows whether or not there will be negative or po sitive correlation in the scatter graphs which I will then draw. These will show the estimates of the line for one individual person plotted against their estimate for the angle. From these scatter graphs you can see whether or not anybody guessed exactly the correct size or length.These things should help me prove or disprove my hypothesis.I have recorded the estimates in a table so as to know which pieces of data I am using they have been highlighted. I am using ICT to do parts of my work as it spreadsheets can work things out extremely quickly, but I will also check and record how I would work things out.First of all I am going to draw some grouped frequency tables, which also show frequency density. This will make the data easier to handle and will mean I can draw a histogram, and grouped frequency graphs. Also, from the frequency tables I am going to find the mean, and I am also going to use standard deviation to find the spread of the number from the mean. If the spread is sma ller, it means that the year group guessed closer to the mean value. An advantage of using standard deviation is that you use all of the data.This is a table to show the Year 9 estimates for the length of line 2.Estimate of length (cm)Frequency (f)Class Width (w)Frequency Density (f) / (w)Mid-Point (x)(f) x (x)3 ? cm ; 43133.510.54 ? cm ; 4.540.584.25174.5 ? cm ; 550.5104.7523.755 ? cm ; 68185.5446 ? cm ; 77176.545.57 ? cm ; 902080Total27140.75The average of results from the above table is the total (f) x (x) column divided by the total frequency. This is 140.75/27=5.21cm. This is 0.61cm longer than the actual length of the line. This is not very much, which means the year nines were quite accurate in estimating the length of the line.To find the spread of this data from the mean I am going to use the equation for standard deviation from grouped data, which is:Efxà ¯Ã‚ ¿Ã‚ ½ (mean)à ¯Ã‚ ¿Ã‚ ½EfSo, for the above table I would do:(33.5à ¯Ã‚ ¿Ã‚ ½)+(44.25à ¯Ã‚ ¿Ã‚ ½)+(54.75à ¯Ã‚ ¿Ã‚ ½)+(85.5à ¯Ã‚ ¿Ã‚ ½)+(76.5à ¯Ã‚ ¿Ã‚ ½)+(0x8à ¯Ã‚ ¿Ã‚ ½)27This equals 28.13194, which I will now subtract the meanà ¯Ã‚ ¿Ã‚ ½ from this. The meanà ¯Ã‚ ¿Ã‚ ½ is 5.21à ¯Ã‚ ¿Ã‚ ½, which gives 27.1441. I will subtract this to give me 0.987844, which I now find the square root of this answer, which is 0.9939. This is the spread of data from the mean. This is quite a low spread.This is a table to show the Year 9 estimates for the size of angle 6.Estimate for Angle sizeFrequency (f)Class Width (w)Frequency Density (f) / (w)Mid-Point (x)(f) x (x)20 ? à ¯Ã‚ ¿Ã‚ ½ ; 301100.124.524.530 ? à ¯Ã‚ ¿Ã‚ ½ ; 35350.6329635 ? à ¯Ã‚ ¿Ã‚ ½ ; 40751.43725940 ? à ¯Ã‚ ¿Ã‚ ½ ; 45751.44229445 ? à ¯Ã‚ ¿Ã‚ ½ ; 50450.84718850 ? à ¯Ã‚ ¿Ã‚ ½ ; 1005500.174.5372.5Total271234The mean of the above table is 1234/27=45.70à ¯Ã‚ ¿Ã‚ ½. This is 12.7à ¯Ã‚ ¿Ã‚ ½ bigger than the actual angle. This is quite a large amount which means that the year 9s were not very accurate in their estimates of angle 6. They we re better at estimating the length of the line.To find standard deviation from this I will do:(124.5à ¯Ã‚ ¿Ã‚ ½)+(332à ¯Ã‚ ¿Ã‚ ½)+(737à ¯Ã‚ ¿Ã‚ ½)+(742à ¯Ã‚ ¿Ã‚ ½)+(447à ¯Ã‚ ¿Ã‚ ½)+(574.5à ¯Ã‚ ¿Ã‚ ½)27This gives the answer of 2303.4, which I will now subtract 45.70à ¯Ã‚ ¿Ã‚ ½ from to give 214.91. I then have to find the square root of this answer. This gives 14.7. This spread is quite high, which means that the estimates given by the year 9s for the size of angle 6 was quite big. You can also see that the year nines had a lower spread of data for the length of line 2.This is a table to show the Year 11 estimates of the length of line 2.Estimate of length (cm)Frequency (f)Class Width (w)Frequency Density (f) / (w)Mid-Point (x)(f) x (x)3 ? cm ; 43133.510.54 ? cm ; 4.590.5184.2538.254.5 ? cm ; 530.564.7514.255 ? cm ; 6141145.5776 ? cm ; 72126.5137 ? cm ; 9221816Total33169The mean of the above table is 169/33=5.12cm. This is 0.52cm bigger than the actual length of the line. This is very low, which shows they were quite accurate in their estimates and were better than the year 9s.To find standard deviation from this I will do:(33.5à ¯Ã‚ ¿Ã‚ ½)+(94.25à ¯Ã‚ ¿Ã‚ ½)+(34.75à ¯Ã‚ ¿Ã‚ ½)+(145.5à ¯Ã‚ ¿Ã‚ ½)+(26.5à ¯Ã‚ ¿Ã‚ ½)+(28à ¯Ã‚ ¿Ã‚ ½)33This gives me an answer of 27.36, from which I will now subtract the meanà ¯Ã‚ ¿Ã‚ ½, which is 5.12à ¯Ã‚ ¿Ã‚ ½. This is 26.22, and subtracted from the precious calculation, the answer given is 1.14, which I then find the square root of, which gives me an answer of 1.07. This is a low spread of data, but not as low as the year 9 estimates of the length of line 2. The year nines estimates were therefore more close together.This table shoes the Year 11 estimates for the size of angle 6.Estimate for Angle sizeFrequency (f)Class Width (w)Frequency Density (f) / (w)Mid-Point (x)(f) x (x)20 ? à ¯Ã‚ ¿Ã‚ ½ 301100.124.524.530 ? à ¯Ã‚ ¿Ã‚ ½ 35650.83219235 ? à ¯Ã‚ ¿Ã‚ ½ 405513718540 ? à ¯Ã‚ ¿Ã‚ ½ 45850.64233645 ? à ¯Ã‚ ¿Ã‚ ½ 511360.547.5617.5Total331355The mean of the above table is 1355/33=41.06à ¯Ã‚ ¿Ã‚ ½. This is 8.06à ¯Ã‚ ¿Ã‚ ½ bigger than the actual angle, which shows that the year 11s again were better at estimating the size of the angle, the year 11s were better at estimating the length of the line though.I will now work out the standard deviation for this:(124.5à ¯Ã‚ ¿Ã‚ ½)+(632à ¯Ã‚ ¿Ã‚ ½)+(537à ¯Ã‚ ¿Ã‚ ½)+(842à ¯Ã‚ ¿Ã‚ ½)+(1347.5à ¯Ã‚ ¿Ã‚ ½)33This gives an answer of 1728.26, which I now subtract 41.06à ¯Ã‚ ¿Ã‚ ½ from to give 42.33. I now have to fins the square root of this to find the final standard deviation. The square root is 6.5. This means the spread is smaller than the spread of the year 9s estimates of angle 6, but the year 11s had a lower spread of data for the line estimates. This means more year 11s guessed closer to the mean for the line. This was also the case for the year 9s.These are the histograms to show these details. The histograms show the spread and how densely populated each group of data is. To draw these histograms, I needed to find the frequency density. The grouped frequency tables on pages 3, 4 and 5 show this. To find the frequency density I did frequency divided by class width.From the histograms, you can see the dashed line. This line shows the actual length of the line, or size of the angle. From the year 11 and year 9 histograms from the angle data, you can see that the year 9s have a wider range of results because they have a very large group of data at the end of the histogram. The density of the group where the actual size of the angle is, is not very densely populated, which means not many people guessed within the correct class.From the histogram for the line data you can see that for the year 9 data the group where the actual length of the line was, had the highest frequency density, but was not the most densely populated. The year 11 data shows that not many people guessed in the correct group as it is not very dense.Cumu lative frequency tables group the data so you can see how much the data has gone up from group to group. A curve can then be drawn, and then a box plot can also be drawn.This is a cumulative frequency table to show the year 11 and the year 9 estimates for the length of line 2. These are drawn so I will be able to find the inter-quartile range of the data after a cumulative frequency curve has been drawn. The median can also be found.Estimated length; 4cm; 5cm; 6cm; 7cm; 8cm; 9cmCumulative Frequency Year 11s31529313133Cumulative Frequency Year 9s3122027This is a table to show the cumulative frequency of the year 11 and year 9 estimates of the size of angle 6.Estimated Size (à ¯Ã‚ ¿Ã‚ ½);30;40;45;50;60;70;100Cumulative Frequency Year 9s1111822252627Estimated size (à ¯Ã‚ ¿Ã‚ ½)3040455060Cumulative Frequency Year 11s112203233From these tables I was able to find the median and modal class intervals. The median class interval shows where the middle estimate is, and the modal class inter val shows which interval has the most estimates in it.These are the median class intervals:AngleYear 9: ;45 class interval. I found this by finding the middle of the total frequency and finding which interval that would be in.Year 11: ;45 class interval again. This shows the median of both results is in the same class interval.This is not the interval where the actual size of the angle would be. The actual size of the angle would be in the group ;40.LineYear 9: ;5 class intervalYear 11: ;5 class interval againThis is the correct group for where the actual length of the line is.The modal class intervals are:AngleYear 9: ;40 class interval. I found this by looking which interval had the most pieces of data in.Year 11: ;50 class interval.The year group who had the majority of estimates closest to the size of the angle were the year 9s, as their modal class was the correct class where the actual angle length could be found.LineYear 9: 6cm class intervalYear 11: 6cm class interval again. These show that the majority of people in both year groups guessed around the same number, but it was not the correct class interval of 5cm.These are the cumulative frequency curves to represent this data. Underneath each curve is a box plot. This shows the inter-quartile range of the data.This curve shows the cumulative frequency of the year 11 estimates for line 2.To work out the median from this curve, you add 1 to the total cumulative frequency and then divide by two. This means, for this particular curve I am going to do 33 + 1 = 34, so 34 / 2 = 17. This means I have to find the 17th piece of data. To do this I find 17 on the y axis, draw a line along until I meet the curve, then draw a line down the x axis, which gives me the median. Also, to find the Inter-quartile range I need to find the lower quartile and upper quartile. To do this I halve the median frequency, and follow along until I meet the curve, then draw a line down to the x axis. This gives me the Lower quartile. I then find the Upper quartile which means I add the lower quartile value from the y axis to the median value from the y axis which gives me the value for the y axis for the upper quartile. I then do as before and draw the lines.The LQ for this curve is approximately 4.5 cm.The median is approximately 5.1 cm.The UQ is approximately 5.7 cm.This means that the IQR is 5.7 4.5 which equals 1.2 cm.This next curve is for the year 9 estimates of line 2. The box plot on this curve actually shows that the lower quartile is below the actual length of the line. This is because people guessed a smaller length than the actual one of the line.The LQ for the last curve is approximately 4.5 cm.The median is approximately 5.2 cm.The UQ is approximately 6.1 cm.This means that the IQR is 6.1 4.5 which equals 1.6 cm.The next curve is for the year 11 estimates of angle 6.The LQ for this curve is approximately 38à ¯Ã‚ ¿Ã‚ ½.The median is approximately 43à ¯Ã‚ ¿Ã‚ ½.The UQ is approximately 47à ¯Ã‚ ¿Ã‚ ½.This means that the IQR is 47 38 which equals 9à ¯Ã‚ ¿Ã‚ ½.The next curve is for the year 9 estimates of angle 6.The LQ for this curve is approximately 37à ¯Ã‚ ¿Ã‚ ½.The median is approximately 42à ¯Ã‚ ¿Ã‚ ½.The UQ is approximately 48.5à ¯Ã‚ ¿Ã‚ ½.This means that the IQR is 48.5 37 which equals 11.5à ¯Ã‚ ¿Ã‚ ½.From these curves I was able to find out that the IQR for the angles in both year groups was higher than the IQR for the line. Also, I found the year 11s had lower IQRs in both of the angle and the line estimates. This could suggest that the year 11s were better at estimating.Percentage error tables show what errors people made. To find the actual percentage error for the above table you have to do a calculation which is:(error/actual length of line) x 100This is a percentage error table for the year 9 estimates of the line and angle.LINE ANGLEEstimate (e)ErrorPercentage error (%)Estimate (e)ErrorPercentage error (%)61.430.43602781.826.21.634.78532060.614.5-0.1-2.173 526.0661.430.433526.0661.430.433526.0650.48.709562187.884-0.6-13.0440721.2150.48.70501751.5261.430.4340721.214-0.6-13.0430-3-9.094-0.6-13.0420-13-39.3950.48.70451236.3650.48.7040721.2150.48.703526.064-0.6-13.043526.0661.430.4340721.214.600.0030-3-9.0950.48.703526.064.5-0.1-2.1740721.214.5-0.1-2.17451236.363.5-1.1-23.91431030.303.5-1.1-23.91431030.303-1.6-34.78501751.524.5-0.1-2.17451236.3661.430.4330-3-9.0950.48.703526.0650.48.70451236.36Total6.6143.48Total238721.21The mean percentage error is worked out by dividing the total percentage error by how many pieces of data there are. So, for the mean of the year 9 line errors, the calculation would be 143.48/27 which equals 5.31%. This is quite a low percentage of error which means that the year 9s were quite good at estimating the line. For the angle it would be 721.21/27 which equals 26.71%. This percentage is so high because someone estimated 95à ¯Ã‚ ¿Ã‚ ½, which means that mean is made higher by this anomalous result. This shows th at the year 9s were better at estimating the length of the line.The next table is for the percentage error of year 11 estimates.LINE ANGLEEstimate (e)ErrorPercentage error (%)Estimate (e)ErrorPercentage error (%)50.48.7040721.2150.48.703526.0650.48.7040721.214-0.6-13.04451236.3650.48.70451236.3650.48.70451236.3650.48.70451236.363-1.6-34.7840721.2150.48.70461339.3950.48.7030-3-9.094-0.6-13.0430-3-9.093.5-1.1-23.9140721.214.5-0.1-2.1729-4-12.1250.48.70451236.364-0.6-13.0430-3-9.094.5-0.1-2.1730-3-9.093-1.6-34.7830-3-9.094-0.6-13.043526.0683.473.9140721.214-0.6-13.0430-3-9.0983.473.9140721.214-0.6-13.04451236.3661.430.43451236.3650.48.70451236.3650.48.703526.0650.48.70501751.524-0.6-13.04451236.364-0.6-13.043526.064-0.6-13.04451236.3650.48.703526.064.5-0.1-2.1740721.2151.430.43451236.3661.430.4340721.21Total6.2134.78Total206624.24The mean for the above table of the line errors would be 134.78/33 which equals 4.08%. This is a relative low percentage which means from the mean there doesn t seem to be much error for the line. For the angle the mean is 624.24/33 which equals 18.92%. This means that from the mean you can see that from the year 11 data, they were better at estimating the length of the line.From these calculations, I have found that the year 11s were better at estimating by finding the mean percentage error, as both of the mean percentage errors for the line and angle, were lower than the year 9 errors.From the percentage error tables I can plot a scatter graph to see how much error there was for the angle compared to the line for both year groups. These graphs were drawn from the actual error made. For example, if someones error for the line was -2, because they guessed 2 below the actual angle size, and their error for the angle was 3, because they guessed 3 above the actual length of the line, then the co-ordinate for their error would be (-2,3).This scatter graph shows the error of the year elevens. If someone had estimated exactly right and therefor e had no error then there mark would be at the point (0,0) on the scatter graph. The point circled in pink is an anomalous result. This is a result which is out of the pattern of the rest of the results.This scatter graph shows the error of the year 9 estimates. The pink circled result is again an anomalous result.Stem and leaf diagrams put the data in numerical order in an easy to read table. This is a stem and leaf diagram to show Angle estimates:Year 9ANGLE 6Year 110295,5,5,5,5,5,5,0,0,030,0,0,0,0,0,5,5,5,5,55,5,5,5,3,3,0,0,0,0,040,0,0,0,0,0,0,0,5,5,5,5,5,5,5,5,5,5,5,63,0,050067859KEY 0 2 9 means that the year 9 estimate was 20 and the year 11 estimate was 29.This is a stem and leaf diagram to show the Line estimates:YEAR 9LINE 2YEAR 115,5,030,0,56,5,5,5,5,0,0,0,040,0,0,0,0,0,0,0,0,5,5,50,0,0,0,0,0,0,050,0,0,0,0,0,0,0,0,0,0,0,0,02,0,0,0,0,0,060,080,0KEY 0 4 0 means the year 9 estimate was 4.0 and the year 11 estimate was 4.0 also.On the stem and leaf diagrams I have highlighted s ome of the values. These are the medians for each stem and leaf diagram. For the Year 11 line, the median is 50, for the year 11 angle it is 40. For the year 9 line the median is 50 and the median for the estimates of the angle by year 9s is 40.I can also find the mode for each group of data. The mode of the estimate of the year 9 line is 5.0 . The mode for the year 11 estimates for the line is also 5.0 . This shows that in both year groups most people guessed the same value, which means, from this mode, you cannot see who is better at estimating.The mode for the year 9 estimates of the angle is 45 and the mode for the year 11s is 40. This shows that the mode for the year 11s is closer to the actual value of 33. This could suggest that the year 11s are better at estimating in this instance.I can also find the range from the stem and leaf diagrams, by subtracting the smallest value from the largest.The range for the year 9 angle estimates is 95 20 which equals 75, which is the range . For the year 9 line the range is 6.2 3.0 which gives you 3.2 as the range.The year 11 range for the angle is 50 29 which equals 21. For the line it is 8.0 3.0 which equals 5.0.From the ranges you can see that the year 9 angle estimates were more spread out than the year 11 angle estimates, but the year 11 line estimates were more spread out than the year 9 line estimates.These tables are made for use in with the scatter graphs. They show Spearmans Coefficient of Rank. This is basically to find the correlation of the data.This table is for the year 9 data.Year 9 Estimate of lineEstimate of angleLine RankingAngle RankingDifference (d)dà ¯Ã‚ ¿Ã‚ ½4.5608.526-17.5306.256.3532725244.5358.580.50.2553517.589.590.2543548-41659517.527-9.590.25440414-101006502523.51.52.2554017.5143.512.256302532248452017.5116.5272.254.6451120.5-9.590.2554017.5143.512.256352581728943548-41654017.517.50053017.5314.5210.2553517.589.590.254.5408.514-5.530.254.5458.520.5-1214454317.517.5003.543117.5-16.5272.2 5450423.5-19.5380.25445420.5-16.5272.2553017.5314.5210.2553517.589.590.2554517.520.5-39TOTALS-3.53494.25Now, to find the Spearmans coefficient of rank you have to use the formula:p = 1 6?dà ¯Ã‚ ¿Ã‚ ½n(nà ¯Ã‚ ¿Ã‚ ½ 1)In this formula, p is the Spearmans coefficient rank of correlation; d is the difference between one item of data and n is the number of items of data.So, for the year nine pieces of data, ?dà ¯Ã‚ ¿Ã‚ ½ = 12.25 and n = 27, so:1 6 x 3494.25 = 1 20965.5 = 1 1.066620879= -0.06662087927(729 1) 19656Therefore, this means that the spread of the year nine data will have almost no correlation at all when plotted on a scatter graph because if the Spearmans coefficient of rank is close to 1 then it means that the data will be strongly positively correlated. If it is close to 0 then it means there will be extremely little or no correlation, and if it is close to -1 it means that there will be very strong negative correlation. This scatter graph shows this:The thick, black lines on this graph show the actual length of the line and the actual size of the angle. If someone had guessed both pieces of data correctly, there estimate would be marked upon the intercept of those two lines. This graph shows that there is very little correlation, which means my Spearmans coefficient rank of correlation was correct. There is an anomalous result on this graph which is when someone has estimated the angle as around 90à ¯Ã‚ ¿Ã‚ ½. This was extremely far away from the actual size.The circled result is an anomalous result. It shows that someone guessed a very different angle estimate to the rest of the pupils. This person didnt really have a lot of error when estimating the line, they estimated only 0.4cm above the actual length but then estimated 57à ¯Ã‚ ¿Ã‚ ½ above the actual angle size, which again indicates that there is no correlation, showing that this person was not too bad at estimating the line length, but were quite bad at estimating angles. This shows th at this person found lines easier to estimate.This is the table for the year 11 data.Year 11 Estimate of lineEstimate of angleLine RankingAngle RankingDifference (d)dà ¯Ã‚ ¿Ã‚ ½54022.516.563653522.51012.5156.2554022.516.5636445827.8-19.8392.0454522.527.8-5.328.0954522.527.8-5.328.0954522.527.8-5.328.093401.516.5-1522554622.532-9.590.2553022.54.51832443084.53.512.253.540316.5-13.5182.254.5291411316954522.527.8-5.328.0943084.53.512.254.530144.59.590.253301.54.5-39435810-2484032.516.51625643084.53.512.2584032.516.516256445827.8-19.8392.0464530.527.82.77.2954522.527.8-5.328.0953522.51012.5156.2555022.533-10.5110.25445827.8-19.8392.04435810-24445827.8-19.8392.0453522.51012.5156.254.5401416.5-2.56.2554522.527.8-5.328.0964030.516.514196TOTALS-19.8392.04Now, to find out the correlation I will substitute the values for the year 11 data into the formula again:1 6 x 4243.74 = 1 25462.44 = 1 0.709181 = 0.29081933(1089-1) 35904This means that when these values are plotted on a scatter graph they will also have extremely little correlation. This shows that people who may have estimated the smallest value for the size of the angle, didnt necessarily estimate the smallest value for the length of the line.This graph shows the year 11 data.Again, the thick, black lines show the actual length of the line and size of the angle. From this graph you can see that the Spearmans coefficient rank was correct, and that the graph has very little correlation. Also, on this diagram, most of the points are relatively near to the line, but there is an anomalous result, which is at the estimate id 8 cm for the line. This persons estimate for the angle was not too inaccurate though. Again the pink circled point is an anomalous result.The lengths of lines are easier to guess than angles.This was my first hypothesis. I feel, through doing many calculations and graphs, that I was able to prove that this hypothesis was correct.Firstly, I drew some grouped frequency tables. From these I was abl e to see that for the year 9s, the mean for the estimate of the lines from the grouped frequency table was 5.21cm, this is 0.61cm longer than the actual length of the line, yet the mean for the year 9s angle estimates from grouped frequency was 45.70à ¯Ã‚ ¿Ã‚ ½, which is 12.7à ¯Ã‚ ¿Ã‚ ½ bigger than the actual size of the angle. There is a lot of difference between these means. Most obviously, the year 9s found it easier to estimate the line, as the difference between the actual length of the line and the mean is much lower. The difference between the size of the angle and the mean is probably higher as there is a result that is 90à ¯Ã‚ ¿Ã‚ ½, which makes the mean much higher. The year 11s mean for the line was 5.12, which is 0.52cm bigger than the actual length of the line. The mean for the year 11s estimates of the angle from grouped data was 41.06à ¯Ã‚ ¿Ã‚ ½, which is 8.06à ¯Ã‚ ¿Ã‚ ½ larger than the actual size of the angle. This shows again that the year 11s found the lines length easier to estimate than the size of the angle.I also did standard deviation which indicates how the data is spread from the mean. For the year 9 angle it was 14.7, which is quite a high spread, showing that the year 9 estimates for the angle size were quite spread apart. For the year 9 line estimates, was 0.99, which means that the results are very compact compared to the mean, which shows that many pupils estimated very close to the mean, showing that the year 9s were better at estimating the lines length.The standard deviation I did for the year 11s showed that the year 11 lines deviation from the mean was 1.07 which is very low, meaning that the results were quite compact. Then, for the angles the spread was 6.5 which is higher than the deviation for the line, showing that the year 11s were better at estimating the line.Next, I drew some histograms, and from these you can see that even though the most densely populated groups were not the groups of 4.5 5 for the line, or 30 35 for the angle, you can see that in the year 11 estimates for line 2, the most densely populated group was 4 4.5cm group. To find this I multiplied the sizes of the groups, in this case 0.5 by the frequency density, 18, which gives 9, which was the highest frequency. And for the angle the most densely populated group was 45 51à ¯Ã‚ ¿Ã‚ ½. Neither of the most populated groups contained the correct estimate for the line or the angle, so it is not possible to tell accurately which one was easier, but you can see that the year 11 estimate for the lines most densely populated group was the group next to the group containing the correct length, whereas this was not the case with the angle.For the year 9 histograms, you can see that the most densely populated group for the angle was joint between the groups of 35 40 à ¯Ã‚ ¿Ã‚ ½ and 40 45à ¯Ã‚ ¿Ã‚ ½ as they both had the highest frequency worked out form the histograms. For the line it was 4.5 5cm group, which is the correct gr oup that contains the actual length of the line. From this you can see that the year 9s were better at estimating the length of the line, which again proves my hypothesis.Next, I drew some cumulative frequency tables and curves. From the year 9 cumulative frequency curve I was able to find the median, which was 5.2cm, this is quite far away from the actual length of the line of 4.6cm. You can also see on the box plot that the actual length of the line is contained at the very edge of the box, nearer the edge of the lower quartile, which means that most year 9s guessed above the length of the line. For the year 9 angle estimates in the cumulative frequency curve you can see that the median is 42 which is very high compared to the actual size of the angle of 33à ¯Ã‚ ¿Ã‚ ½. This means that the year 9s box plot for the angle didnt contain the actual size of the angle in it. This is because someone estimated 90à ¯Ã‚ ¿Ã‚ ½, which is very high. This means that the year 9s, again found th e line easier to estimate.The cumulative frequency curves for the year 11s estimates of line 2 show that the median from the curve was 5cm. This is 0.4cm bigger than the actual length of the line. The actual length of the line is contained in the box, but at the very edge of the lower quartile. This again shows that most people estimated over the length of the line. For the year 11 angle cumulative frequency curve, the median was 43à ¯Ã‚ ¿Ã‚ ½, which is 10à ¯Ã‚ ¿Ã‚ ½ over the actual size of the angle. The actual size of the angle again is not in the box, showing that many people again guessed above it, which leads to show that the year 11s found the line easier to estimate.Next I drew some percentage error tables. For the year 9 line the mean error was 5.31%, which is relatively low, showing that there was not much error at all. The percentage of error for the angle though was 26.71% which is much higher than the percentage error for the line, meaning that the year 9s had less err or when estimating the length of the line.For the year 11 tables, I was able to find the mean percentage error of 4.08% for the estimating of the line, which is rather low showing that the year 11s did not make much error whilst estimating the line. However, their percentage error mean for the angle was 18.92 which is much higher than the line error percentage, showing that the year 11s were better at estimating the length of the line as they had less error.From the scatter graphs drawn by the error you can see that there is no correlation between the errors.From the stem and leaf diagrams, you can see that the median for the year 9s line estimate is 5.0cm, which is 0.4cm above the actual length of the line, and the year 11 median for the angle was 40. This is 7à ¯Ã‚ ¿Ã‚ ½ above the actual size of the angle, meaning that the year 11s were better at estimating the line. The numbers for the median of the year 9s from the box plots were the same as the year 11s showing that the year 9 s were better at estimating the length of the line also.I then did standard deviation to find out what correlation the scatter graphs would have when I drew them. From doing standard deviation I was able to see that for the year 9 scatter graph there would be extremely little correlation at all, as the answer I got after doing the equation for standard deviation, which is shown on page 17, was -0.066620879, this means that5 there would be VERY slight negative correlation, but hardly any at all, meaning that if a year 9 isnt very good at estimating the length of a line, then they are not necessarily bad at estimating the angle size.For the year 11s the answer I got from working out the standard deviation was 0.290819, which means that there would extremely slight positive correlation, but hardly any at all really. This means that if they were really good at estimating the line, they were not necessarily good at estimating the angle size. The scatter graphs show this data.Overall, I f eel I have managed to prove the hypothesis of the length of lines is easier to guess than angles as correct through many calculations and graphs.Year 11s will be more accurate at estimating.This was my second hypothesis, and through the calculations I have done I feel I have managed to come to a conclusion of proving or disproving this hypothesis.Firstly, I made some grouped frequency tables, which I then found the mean from. The mean for the year 11s estimates of the line from the grouped frequency was 5.12cm which is 0.52 above the actual length of the angle. The mean for the year 9 estimates was 5.21 which was 0.61cm above the actual length of the line. This shows that as the mean was closer to the actual length of the line, the year 11s were better at estimating the length of the line in this case. For the angle estimates from grouped frequency tables, I was able to see that the year 11 mean from the grouped frequency was 41.06à ¯Ã‚ ¿Ã‚ ½ which is 8.06à ¯Ã‚ ¿Ã‚ ½ above the act ual angle size, whereas the year 9 mean from the grouped frequency tables for the angle was 45.70à ¯Ã‚ ¿Ã‚ ½ which was 12.7à ¯Ã‚ ¿Ã‚ ½ higher than the actual size of the angle. This means that the year 11s were better at estimating the size of the angle than the year 9s were.Next, I found the standard deviation for both year groups. I used the equation on page 3 to do this. For the year 9 line estimates I found out that the spread of the data from the mean was 0.9939 which is quite a low spread, meaning the estimates were quite close together. For the year 11 estimates for the length of line 2, the deviation of the estimates was 1.07, which means that the year 9 estimates for the length of line 2 were less spread out than the year 11s.For the year 9 estimates of the angle, the spread from the mean was 14.7 which was quite high, showing that the results were quite spread out. For the year 11 estimates of the angle, the standard deviation was 6.5 which means there was quite a lot of spread, but less than the year 9s meaning that the year 11 results were less spread out in this case.After this, I drew some histograms. From the year 9 histograms you can see, for the line, that the most densely populated group was 5 6 cm which, is not the group where the actual length of the line was contained. For the year 11s, the most densely populated group was also the 5 6 cm group which was again not the correct group where the actual length was, showing that both the majority of the year 9s and year 11s guessed that the line was in the region of 5 to 6 cm.For the year 9 histogram for the angle, the most densely populated groups was joint between 35 40 and 40 45, which did not contain the actual size of the angle. For the year 11s the most densely populated group on the angle histogram was 35 40, which again did not contain the correct size of the angle, meaning that the majority of both year groups estimated in the incorrect group.I then drew some cumulative frequency curves. These showed me the frequency of the data in the form of a curve. For the year 9s, from the curve for the line estimates, I could see that the inter-quartile range of the data was 1.6cm and the median was 5.2cm. For the year 9s curve for the line the inter-quartile range was 1.2cm and the median was 5.1cm. From these results you can see that the year 11s had both a lower median and a lower inter-quartile range. This could suggest that they were better at estimating.For the angle cumulative frequency curve for the year 9s the inter-quartile range was 11.5à ¯Ã‚ ¿Ã‚ ½ and the median was 42à ¯Ã‚ ¿Ã‚ ½. For the year 11s the inter-quartile range was 9à ¯Ã‚ ¿Ã‚ ½ and the median was 43à ¯Ã‚ ¿Ã‚ ½, this means that the year 11s had a lower inter-quartile range value, but the year 9s had a lower median value.After drawing cumulative frequency curves, I was able to draw some box plots. From these I was able to see the inter-quartile range and median easily.For the year 9 box plot f or the line I was able to see that between the highest result and the upper-quartile there is very little difference. The upper quartile was 6.1cm and the highest result was 6.2cm. This shows that the many people estimated higher up on the scale as between the lowest estimate of 3cm and the lower quartile of 4.5cm there is quite a large gap.For the year 11 box plot of the line, I was able to see that the data is quite evenly spread as the box plot is relatively in the middle of the lowest value of 3cm and the highest value of 8cm. The actual length of the line is contained with in the inter-quartile range box, but, towards the very end of the lower quartile side, meaning that most people estimated above it.For the year 9 box plot of the angle estimates I was able to see that the actual size of the angle is not contained within the inter-quartile range. This is because many people guessed above the correct size of 33à ¯Ã‚ ¿Ã‚ ½, meaning that it was not contained within the inter-qua rtile range.The year 11 box plot for the angle showed that many of them also estimated above the size of the angle of 33à ¯Ã‚ ¿Ã‚ ½, as it is again not contained in the inter-quartile range. After analysing these box plots, I do not feel that they have helped me to prove or disprove my hypothesis.Next, I drew some percentage error tables. From these I was able to see what error each individual made in their estimates. I then found how much error they made as a percentage. Overall, for the year 9 estimates of the line, the mean percentage error was 5.31%, which is quite low, means that they did not make too much of an error overall. For the year 11 estimates of line two, the mean percentage error was 4.08%. This is a lower percentage of error than the year 9s meaning that overall, the year 11s made less error in estimating the length of the line.For the year 9 estimates of the angle the mean percentage error was 26.71% which is quite high. This is because there was an anomalous resu lt of 95à ¯Ã‚ ¿Ã‚ ½, which means that the overall mean percentage error value will be higher. For the year 11 estimates of the angle, their mean percentage error was 18.92%, this is still quite high, but lower than the year 9s mean percentage error for the angle meaning that the year 11s had less error in estimating the angle overall again.Next, I drew some scatter graphs which showed how much error someone had made, for example if some had estimated 2à ¯Ã‚ ¿Ã‚ ½ above the actual angle size, and 0.3cm below the estimate of the line, their coordinates would be (-0.3,2). From the scatter graphs I was able to see that there was not really any correlation in either the year 11 or year 9 scatter graphs. Again, after analysing these I do not feel that they help me to prove or disprove my hypothesis.After this, I drew some stem and leaf diagrams. I was able to find the median and mode from these. They also showed me the data in a table, showing each and every result.For the year 9 line e stimates I was able to work out that the median was 5.0cm which was also the median for the year 11s. This means that when all the data is put in consecutive order, that both the year 9s and the year 11s had the same middle estimate. For the angles I was able to see that the median for the year 9s was 40à ¯Ã‚ ¿Ã‚ ½, and the median for the year 11s was also 40à ¯Ã‚ ¿Ã‚ ½. This means that again they had the same middle estimate. I do not feel that these have helped me to prove my hypothesis.Next, I did the spearmans coefficient rank. This shows what correlation the data will have when plotted on a scatter graph. For the year 11s I was able to see that after working out that the correlation would be hardly visible, but would be extremely slightly positive, as the answer I got after working out the spearmans coefficient rank was 0.290819. I then plotted my points on a scatter graph and found out that this was correct. I then worked out the spearmans coefficient of rank for the year 9s . This gave me an answer of -0.066620879, meaning that there would be a very slight negative correlation. I plotted my points on a graph and was able to see that again I was correct. I was shown that for both year groups the estimate for the line didnt necessarily correlate with the estimate for the angle. For example, my results did not show that if someone estimated high for the angle size, they did not necessarily estimate high for the line length.Additionally, from the scatter graphs I was able to see that there were some anomalous results. For example there was a year 9 who estimated the angle at being 95à ¯Ã‚ ¿Ã‚ ½, whereas they estimated the line at being 5cm which showed that they did not estimate too extremely for the length of the line. I do not feel these scatter graphs assisted me in proving my hypothesis.Overall, I feel I have been able to prove this hypothesis as correct through the calculations which referred to it.I think all of my calculations and diagrams were cor rect as they all led to the same conclusion, and through checking my answers I found that they were correct. I think there were not really any major anomalous results, apart from the ones previously mentioned and shown in my calculations.One problem I did have was finding the standard deviation, but I realised this was because I was trying to find it from grouped data, and therefore needed a different formula, and after getting the formula for grouped data I found it a lot easier to do.I managed to prove my hypotheses were correct in most instances and I managed to show many different types of calculations in proving my hypotheses.

How TNT Pop Its Snappers Work

How TNT Pop Its Snappers Work TNT Pop Its belong to a class of novelty fireworks collectively called bang snaps. Similar products are called snap-its, poppers, and party snaps. Kids have been using them for pranks and celebrations since the 1950s. In case you were wondering, Pop Its dont contain TNT. That is simply their brand name. Pop Its are trick noisemaker rocks, commonly seen around the 4th of July and Chinese New Year, that pop when they are stepped on or thrown against a hard surface. They look like little paper-wrapped rocks, which, in fact, is what they are. The rock is gravel or sand that has been soaked in silver fulminate. The coated grains are twisted into a piece of cigarette paper or tissue paper. When the bang snap is thrown or stepped on, the friction or pressure detonates the silver fulminate. Pop its can also be ignited, although its not particularly safe to set them off in your hand. The tiny explosion makes a sharp snap that sounds a bit like that of a cap gun. Chemistry of Pop Its Silver fulminate (like mercury fulminate, which would be toxic) is explosive. However, the quantity of fulminate in Pop Its is very small (about 0.08 milligrams) so the little exploding rocks are safe. The sand or gravel moderates the shock wave produced by the detonation, so even though the sound is loud, the force of the pressure wave is fairly minor. Snapping one in your hand or stomping it with bare feet can hurt, but is unlikely to break the skin. The sand or gravel isnt propelled very far, so there isnt danger of the particles acting as projectiles. Generally, Pop Its and related products are considered safe for use by children. While poisonous fulminates of other metals would produce a similar effect, they arent used in commercial products. Make Pop Its Yourself Fulminates are easily prepared by reacting metal with concentrated nitric acid. You dont want to go making this in any quantity yourself because the fulminate is shock sensitive and pressure sensitive. However, if you decide to make do-it-yourself Pop Its, the silver fulminate is more stable if flour or starch is added to the crystals during the filtering process. You can coat sand with silver fulminate, wrap it in paper, and use it in the traditional way. Bigger is not better - be safe.

Journal Essay Example | Topics and Well Written Essays - 1250 words - 1

Journal - Essay Example Marketing management bases on the concept of situation analysis in which the manager has to keenly analyze and closely monitor the firm so that everything runs parallel to the firm’s objectives and mission. Since it is a broad field, situation analysis divides itself into the economic, competitive, cooperative, legal, social and political environments. The economic environment It is a major determinant of how the firm survives in a competitive market. This type of environment can bring with it marketing opportunities or constraints. For example, such factors as high inflation and unemployment can limit the size of the market that can afford to purchase a firm’s top-of –the-line product (Peter and Donnelly 17). The competitive environment Firms are after a similar raw material and target at same consumers. In this environment, the management must look out for competing firms, drive competitors out of the industry and aim at offering value sensible products to the consumers. Political environment It influences how the public views the product. It composes of the business critics, the public and other organizations. To guard the corporation image, the management must satisfy the standards set to avoid criticism. ... Operations management functions The functions are categorized under design and control issues (Mahadevan 16). For the design issues, the functions are realized in product and design development. This is a major importance since it facilitates creativity in production to withstand external competitions. In addition, there is improved quality management, which helps build trust with customers. Designing is important when locating and making layouts of facilities that enables efficiency in production. For control issues, operations management is a guide for forecasting, as it understands the flow and trends of products. This helps in controlling production such that there is neither surplus nor deficit. Supply chain management is put under control since it depends on the operations management decisions. Still, the operations management helps guide the maintenance management because the operations determine how frequent the maintenance practices are carried out. With all these summed up, there is a continuous improvement of operations in a company. The operations management faces competitive pressure. This is because of technological advancement today. This can be attributed to be a major challenge. On the same note, the pressure can be from the economic reforms. Organizational design Organizational design involves two complementary problems: how to partition a big task of the whole organization and how to coordinate the subunits so that they fit together (Burton et al). The problems make organizational design a continuous executive process that requires short-term and long-term resolutions. Since it is a continuous process, a systematic approach reveals what happens Step 1: getting started Every firm has a goal and mission

Unethical Desion in business Essay Example | Topics and Well Written Essays - 750 words

Unethical Desion in business - Essay Example what Alan Greenspan called the â€Å"increasingly complex financial instruments† that were supposed to have built â€Å"a far more efficient, flexible and resilient financial system† were actually tools designed to circumvent the banking regulatory system meant to ensure safety and prudence in the first place (Lewis et al., 2010:79). The bankers behind them were not motivated by any desire other than greed for profits, and their greed cost hundreds of thousands of people worldwide their homes, jobs, and the security of their families. In earlier times and even today in many cultures, the image of a businessman connotes shrewd selfishness that will not hesitate to pry the last dollar from an unwitting customer’s fingers. In many instances, the impression is well-justified, prompted by the oft-used phrase: â€Å"It’s only business† in explaining why the hapless customer should find himself short-changed. The multi-million dollar golden parachutes CEOs of the failed banks awarded themselves with before abandoning the ship of drowning investors are perfectly legal, they argue: it’s just business, as if that were sufficient excuse to avoid the norms of ethical behaviour. It is often thought that unethical behaviour in business is caused by the lack of time to ponder the repercussions of a decision that must be made in haste. That is not so, according to a recent study. Zhong, et al. (2010) found just the opposite, that the greater the time for deliberation, the less ethical the decision tends to be. This appears to contradict all known earlier philosophies that the time to reason ensures ethical choices. The experiment performed in the study, however, seems to suggest that when given the freedom to consult their consciences before acting, instead of simply following the rules, one is persuaded to rationalize his actions, to provide some â€Å"good† to explain why an unethical decision (usually more beneficial to himself) could be made. In simple words, the

Google in China Essay Example for Free

Google in China Essay Google is the fastest growing Internet search engine company. Google’s mission is â€Å"to organize the world’s information and make it universally accessible and useful.†(International Business: Competing in the Global marketplace, pg 148-149) They have a mantra of â€Å"Don’t be Evil.† Google started this mantra to be the main message to show consumers they would not compromise the integrity of its search results. This case reviews the situation under which Google was required to censor its content and chose to launch its new search engine site. The case explains the role of the Chinese government and its regulations in the Internet market which had a negative effect on Googles operations in China. In 2000, Google started a Chinese language service. This service was operated from the United States. Chinese authorities blocked the site in 2002 because China censors information to their citizens. This block surprised Google’s managers. This was a challenge the managers did not plan on. If they done their research of the Chinese Government and culture prior to launching the Chinese language service, they would have known the block would be inevitable and they could have tailored their service to the Chinese regulations, culture, and laws. Google knew China was an advantageous business and they would need to adapt their service in order for it to be acceptable and profitable. Google also had to move the Chinese operations to China. Operating from the United States caused slow connection speed and hinder their operation and growth. This was a good move because it enabled Google to employee Chinese citizens who would be able to help understand and adapt to the Chinese laws, regulations, and censorship demands. Google managers made a mistake by not researching their target market. However, they acted quickly in learning and correcting this mistake. Google still offered Chinese citizens a better search engine, but it was not without censorship. The Google search engine offers more results than its competitors, Yahoo, Microsoft’s MSN, and China’s own company, Baidu. Google states Chinese consumers will â€Å"get more information on their site, though not quite all of it.† (International Business: Competing in the Global marketplace, pg 148-149) In 2006, Google had 30 percent share of China’s internet search engines. Baidu had 40 percent. This left another 30 percent split between Yahoo and Microsoft’s MSN search engines. These percentages are good, especially when one considers Yahoo and Microsoft had entered the Chinese search engine market prior to Google. Baidu has several advantages over Google that are mostly associated with it being a Chinese based company, the search engine has â€Å"competence in pinpointing queries in the Chinese language† (Yin Yulin, 2010, p. 4). Government relations with China are precarious for businesses effectiveness. Google did not have a clear understanding of what they would be involved in. China has become more supported and self-assured due to its increasing economic significance. They are more reluctant to be pressed by Western governments or companies into changing its long term regulations and censorship. Because of this aspect, China does not yet comprehend global strategies and the importance of global public relations. This causes them to be more rigid in their international business dealings. All-in-all, Google has been able to grow successfully in the Chinese search engine market and maintain the number two spot (behind Baidu) in China despite their lack of early research on the Chinese culture, governmental regulations, and laws. References International Business. Competing in the Global Marketplace, Seventh Edition, Chapter 3: Differences in Culture ISBN: 9780073381343 Author: Charles W. L. Hill copyright  © 2009 McGraw-Hill, a business unit of the McGraw-Hill Companies, Inc.

Many Types of Wrestling :: essays research papers

Wrestling Thesis statement: Free style, Professional, Greko Roman, and Collegiant wrestling have very different rules and styles. I. Free style wrestling A. Rules B. Style II. Professional wrestling A. Rules B. Style III. Greko Roman wrestling A. Rules B. Style IV. Collegiant wrestling A. Rules B. Style Wrestling is broken into four different types based on rules and style; Free style, Professional, Greko Roman, and Collegiant. Free style is usually started after school is let out for the summer. The rules of Free style wrestling are pretty simple. Both wrestlers start in the standing position for all three rounds. Each round is two minutes long, and the person with the most points at the end of the third round wins. Free style wrestling is done on a mat, approximately two inches thick and is half the size of a basketball court. The out of bounds area on the mat is marked by a circle; so no one gets hurt by being thrown off the mat. There are several ways to score points, takedowns, throws, and pins. Takedowns are when one wrestler has the other wrestler under control on the mat, all four extremities are touching the mat. In Free style, after a takedown both wrestlers start back at the standing position. Takedowns are worth one point, because using the legs is not favorable in Free style. Throws are exactly what is sounds like, one wrestler throws the other one. Two to four points can be awarded depending on the height of the throw. The higher the more points. After a throw both wrestlers start back at the standing position. A pin in Free style is when one wrestlers shoulder blades roll on the mat. You do not have to hold a wrestler down for a count of three to get a pin in Free style. Free style is basically practice for the Collegiant wrestling season.   Ã‚  Ã‚  Ã‚  Ã‚  Professional wrestling is done in a boxing ring, the rules are vague, but the sport is very entertaining. They can hit each other with chairs, body slam from the top ropes, and even throw each other out of the ring! I think the only rule they have is no biting. Professional wrestling is done for the entertainment of others.   Ã‚  Ã‚  Ã‚  Ã‚  Greko Roman wrestling also has three rounds and is played on a mat. The real difference in Greko Roman is that you can not use the legs at all. To score points in this type of wrestling you must throw your opponent. The higher you throw your opponent the more points you receive. You can win if you throw

Maze Learning

MAZE LEARNING 1 MAZE LEARNING Ana Iqbal Mirajkar Bahria University BS-04 MAZE LEARNING 2 Abstract This experiment was conducted to uncover the underlying principles of transfer of training in maze learning. The aim was to see if transfer of training facilitated maze learning. It was assumed that practice of one maze would assist the chances of transfer in another and that participants who had prior knowledge of mazes would perform better. A sample of 56 students was chosen conveniently from Bahria University.All participants performed the same experiment on maze A and B, which is they traced a maze twice with the experimenter’s help, had a break of ten seconds and then had five minutes to find the goal. The results were analyzed using percentages. The findings of the results indicated that practice of one maze assists transfer of training on the other and that participants with prior knowledge had more successful trials than the ones who did not. Thus, both hypotheses were pro ved. Key words: maze, learning, memory, cognitive mapping MAZE LEARNING Learning is a relatively permanent change in behavior brought about by experience (Feldman, 2009).Peter Gray, a psychologist, defines learning as any process through which experience at 3 one time can alter an individual's behavior at a future time. Hence learning can be anything that brings about a change in one’s behaviour, or another definition common to all theories of psychology would describe simply a stimulus that generates a response(S-? R) (Herbert Terrace). Learning has been an important area of research in psychology; psychologists have done extensive research on how human beings acquire learning and what factors facilitate learning.One such experiment is done by Ivan Pavlov where he introduced the concept of classical conditioning and concluded that learning occurs gradually through pairing and association (Pavlov). Whereas a gestalt psychologist by the name of Wolfgang Kohler concluded that n ew behaviour is learned due to insight. According to Frederic Vestor there are four types of learning. The first being auditive learning which is learning by using the auditory channels that is using the ear to listen and mouth to speak. Second is visual learning that is learning using the eyes.Haptic learning is the third type of learning which occurs by touching and feeling and the fourth type is learning through the intellect. Training is the acquisition of knowledge, skills, and competencies as a result of the teaching of vocational or practical skills and knowledge that relate to specific useful competencies. Areas that use training extensively are job training such as worker endowment and physical training for sports. Transfer of training was originally defined as the extent to which learning of a response in one task or situation influences the response in another task or situation (Adams, 1987).While Thorndike and Woodworth (1901) predicted that transfer would occur as long as the aims, method, and approaches used for the learning task were similar to the transfer task. They found support for the generalization of responses when there was similarity in the stimuli and responses in the learning and transfer environment. Types of transfer of training are positive which means previous training facilitates new training such as learning to add numbers in math courses helps when one learns multiplication.Negative transfer occurs when previous training hinders new training, whereas zero transfer is when previous trainings have no effect on new ones. Wolfgang Kohler would say that learning occurs through sudden insight while Thorndike would contradict by saying that it happens gradually over a long period of time. Generally it is noted that learning is both intentional and unintentional and has no specific time requirements. That is MAZE LEARNING one can learn in a day or can take months. Whereas training is usually intentional and there are certain time bound aries for training.Furthermore, learning focuses on achieving permanent 4 changes in behaviour while training focuses on the acquisition of new skills and knowledge with training interventions being event driven. Memory refers to the processes that are used to acquire, store, retain and later retrieve information (Kendra Cherry). The process of forming a memory is composed of three components encoding, storage and retrieval. In order for pieces of information to make sense the brain encodes all the information to form memories and stores it.A memory, when brought into consciousness is known as retrieved memory. Memories can be of three types; sensory memory that is collected from the first hand experiences and is very brief. Short term memory is what is in the conscious awareness, whereas long term memory is what is not in the conscious awareness and might have to be retrieved, according to Freud short term memory would be the conscious and long term memory the unconscious. Ebbingha us, who was a pioneer of the experimental study of memory, did extensive research on memory, memory formation and memory decay.Through his experiments he devised the forgetting curve of memory which revealed a relationship between forgetting and time. He suggested that information, initially, is often lost very quickly after it is learned but after a certain point the amount of forgetting levels off. This indicates that information stored in long-term memory is surprisingly stable. (Hermann Ebbinghaus) Labyrinth is a term in Greek Mythology, which basically denotes a maze in which the Minotaur was confined (The Free Dictionary).The most ancient of labyrinths are Cretan labyrinths that are surrounded by an aura of mysticism and skepticism, this was the elaborate structure designed to hold Minotaur. Next are the Egyptian Labyrinth and the Leminian Labyrinth which are more densely routed and complex than the Cretan Labyrinth. Although the true origins of the mazes and labyrinths probab ly go back to Neolithic times, the earliest mazes were actually parts of architectural monuments built in Egypt and on Crete about 4000 years ago (Christopher Berg).Edward Chase Tolman, a pioneer in the areas of learning and motivation, claimed that everything important in psychology can be investigated in essence through the continued experimental and theoretical analysis of the determinants of rat behavior at a choice-point in a maze. A maze is defined by Webster as a confusing, intricate network of MAZE LEARNING 5 winding pathways; specifically with one or more blind alleys. Furthermore, one could perceive a maze as a complex structure with a series of interconnecting pathways that eventually has to be solved by pursuing a goal.The term is also used to refer to a graphical puzzle that replicates the maze on a two dimensional medium (S. E. Smith). Mazes, in psychology, have contributed greatly to understanding complex human behavior. Moreover, maze studies have helped uncover asto unding principles about learning that can be applied to many species, including humans. The fact that researchers have even used mazes to figure out if men and women are different in the way they perceive suggests the important role mazes have played throughout. In this context a study was carried out by B.Jones that looked at trial and error learning in humans using a virtual maze and at looked at the gender differences where the participants were tested using the Online Psychology Laboratory Maze. Another study which attempted to uncover if multiple trials allow a researcher to determine how ability can develop and change over trials and that the importance of task components fluctuates during the stages of learning (O'Neill, 1978). The findings gave the impression that repeated trail can help the participant develop the knowledge of the maze and make fewer errors.Yet one more research finding on mazes indicated that no matter how well the maze is learned, the subject will never a ble to dispense with sensory guidance and that there is throughout this type of functioning a close cooperation between sensory and motor adjustments (Ailene Morris). There are two main categories of mazes which are then further subdivided into various types. A Unicursal maze is without branches, it has no dead ends and there is one path that leads to the end whereas, a multicursal maze is one with branches and dead ends. Among the various types of mazes are Blind Alleys are mazes that have a branch that is a dead end.Simply-connected mazes have pathways that never re-connect with one another, so every path leads to additional paths, a fork, or to a dead end and there is only one solution to a simply-connected maze. A multiplyconnected maze contains one or more passages that loop back into other passages, rather than leading to dead ends. A more complex form of the multiply-connected maze is the braid maze. A weave maze has pathways that go under and over each other and can be in mu ltiple dimensions, while a logic maze must be navigated by adhering to logical rules in addition to following its passages such as symbols or following colour schemes.A Plainair maze, however, is a maze on something other than a flat surface. For example, a maze painted on the outside of a cube or sphere. MAZE LEARNING A principle that is derived from the extensive study of mazes is known as cognitive mapping; 6 making a mental picture of one's physical or spatial environment (APA). A cognitive map allows one to construct and accumulate spatially defined images whose function is to enhance recall and learning of information. This type of spatial thinking can also be used in non-spatial tasks. Chaining is a behaviour technique that involves breaking a task down into smaller components.The simplest or first task in the process is taught first, and then after this has been learned, the next task can be taught. This continues until the entire sequence is successfully chained together (K endra Cherry). Maze learning is an example of a successive chaining, when animal runs down a maze it chains the route through the subsequent goals and dead ends all in all the entire stimuli present in the environment gives the animal clues and make his cognitive map (Terrace). The aim of this study is to see if transfer of training facilitates performance.It is assumed that the practice of one maze will facilitate the chances of transfer of training on the second maze and that participants having knowledge of practical will have more successful trials than participants who do not have any prior knowledge. Method Participants: There were two groups of participants that participated in the study. Group 1 composed of 28 people who had no prior knowledge of maze leaning. While Group 2 composed of 29 participants who had prior knowledge of maze learning. The total sample was that of 56 students who were chosen conveniently from Bahria University.The design of the experiment was independ ent measures design. Materials: Match box, scissor, glue, mazes A, stop watch and a blindfold. Two mazes were extracted from the internet and the participants of group 2 constructed the entire maze using match sticks to cover all the branches and boundaries of the maze. It was later discovered that both mazes were multicursal and simply connected. Procedure: The experiment was conducted in the experimental lab, with controlled conditions. In the first phase of the experiment participants from group 1, who had no prior knowledge of maze learning, were tested.The experimenter blindfolded the participant and traced their finger, twice, along maze A (in some cases a thin object such as a pen or pencil was used). During the whole procedure it was tediously made sure that the participant did not see the mazes. Following MAZE LEARNING 7 this the participant was given a ten second break and then told to complete the maze again with no help from the experimenter this time. After given five m inutes to complete this maze, the participant was told to stop and the blindfold was undone for two minutes.The same procedure was then followed for maze B that is tracing twice with the experimenter’s help, a break and then five minutes for the trial for maze B. Throughout the experimenter observed the errors made and the progress of the participant. In the second phase of the experiment the participants from group 2, who had prior knowledge of maze learning, were tested following the exact same procedure that is tracing twice maze A and then later maze B with an experimenter’s help, a break of ten seconds, then five minutes for the trial for maze A and later maze B.Results Table I Showing results of Maze A of Group 1 Participants 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Successive Trials 1 3 3 2 4 0 1 1 4 2 5 0 1 4 Errors 0 4 7 3 0 0 3 0 0 1 0 5 14 0 MAZE LEARNING 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 4 5 2 1 1 0 0 2 0 1 0 4 0 3 10 4 2 4 0 3 10 8 20 20 7 10 8 8 Total 5 2 146 Table II Showing results of Maze B of Group 1 Participants 1 2 3 4 5 6 7 8 9 Successful Traits 5 2 3 1 0 0 0 0 3 Errors 10 0 4 4 0 3 5 2 0 MAZE LEARNING 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2 5 0 8 4 3 2 2 5 2 0 0 0 2 2 2 0 3 2 1 4 13 0 15 0 9 0 20 0 11 3 2 2 25 1 3 2 9 Total 58 148 Table III Showing results of Maze A of Group 2 Participants 1 2 3 4 Successful Trials 5 0 3 3 Errors 1 2 3 3 MAZE LEARNING 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2 3 1 1 7 7 3 4 3 5 4 3 4 3 1 1 4 1 2 2 2 3 2 0 0 8 4 2 3 1 12 4 1 0 2 2 7 4 5 4 1 1 14 0 1 1 5 0 10 Total 79 91 MAZE LEARNING Table IV Showing results of Maze B of Group 2 Participants 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Successful Traits 5 0 0 6 4 8 10 1 10 11 7 5 3 7 7 2 8 5 1 4 4 2 1 3 2 4 Errors 0 4 0 4 0 0 0 3 0 1 5 7 0 3 0 0 3 3 0 2 0 2 1 0 5 0 1 MAZE LEARNING 27 28 0 5 3 0 12 Total 125 46 Calculations:- = 41. 7% = 58. 2% = 35. 03% = 64. 96% MAZE LEARNI NG Graph I Showing results of comparison between Maze A and Maze B 13 Comparison between both the mazes 42% Maze A Maze B 58% Graph II Showing results of comparison between Group 1 and Group 2 (c and d) Comparison between both the groups 35% Group 1 65% Group 2 MAZE LEARNING Discussion It was proved that practice of one maze facilitates the transfer of training on the second maze 14 hich meant that most of the participants performed well on maze B as compared to maze A. An interesting research by Edward Tolman on rats and mazes showed that once the rats knew where there goal in the maze was, they could find their way through the maze. Thus, Tolman’s and this research show that people form a cognitive map of the spatial layout of the situation rather than just leaning to make a series of responses. However, one single most undermining factor that could cause this is the carry over effects the participants might have carried over from maze A.Furthermore, there might been quite a many extraneous variables present in the environment that the experimenter failed to control; hence, they became confounding variables. These include noise distractions, the close seating arrangement of the participants and experimenter bias. It was further noted that even though both mazes were multicursal participants found maze B relatively easier and more straight forward than maze A, pointing more towards the fact that practicing on one maze improved their performance.Likewise, the participants who had prior knowledge of mazes performed better than the participants who did not. This meant that hypothesis 2 was also proved. David Ausubel a pioneer in educational psychology who emphasized on prior learning said â€Å"If I had to reduce all of educational psychology to just one principle, I would say this: The most important single factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly. The results of this research highlight the importance of prior learning. Nevertheless, the participants of group 2 were also the ones who constructed the maze, which meant that they possibly brought forward transfer effects. Moreover, the participants in group two were in a more comfortable setting than the participants in group one who were not in their comfort zone. Besides, there were four students who were not from the psychology department and might have been anxious because of the new and unfamiliar place and setting.In addition to this some participants used a pencil, pen or a sharp object to complete the maze instead of their fingers, which meant less tactile experience and learning and might be a contributing factor as to why group 1 performed poorly. MAZE LEARNING References: American Psychological Association. (2013). Dictionary. com Unabridged. Retrieved from http://dictionary. reference. com/browse/cognitive map Ausubel, D. (1968). Educational implications of concept mapping. Joseph D. Novak & D. Bob Gowin (2002 ). Learning how to learn (pp. 40). UK, Cambridge University Press. Berg, C. 2011). The History of Mazes and Labyrinths. Amazing Art. N/A. Retrieved from http://amazeingart. com/maze-faqs/ancient-mazes. html Cherry, K. (N/A). An Overview of Memory. Memory. N/A. Retrieved from http://psychology. about. com/od/cognitivepsychology/a/memory. htm Ebbinghaus, H. (1885). Memory: A Contribution to Experimental Psychology. Classics in the History of Psychology. N/A. Retrieved from http://psy. ed. asu. edu/~classics/Ebbinghaus/index. htm 15 Eddie, W. L. & Danny, C. K. (2001). A review of transfer of training studies in the past decade. Personnel Review, Vol. 0 No. 1, 102-118. Retrieved from http://www. owlnet. rice. edu/~ajv2/courses/12a_psyc630001/Cheng%20&%20Ho%20(2001)%20 PR. pdf Feldman, R. S. (2009). Psychological Approaches to Learning, 177. Retrieved from http://www. studymode. com/essays/Psychological-Approaches-To-Learning-730466. html Jones, B. (2011). Gender Difference-Mazes, 09. Re trieved from http://www. studymode. com/essays/Gender-Difference-Mazes-774551. html Morris, A. (1994). A Descriptive Study of Maze Learning, 67-69. Retrieved from http://digital. library. okstate. edu/oas/oas_pdf/v25/p67_69. df Terrace, H. (2010). The Comparative Psychology of Serially Organized Behavior. Comparitive Cognition and Behaviour Reviews, Vol. 5, 23-58. Retrieved from http://psyc. queensu. ca/ccbr/Vol5/Terrace. pdf MAZE LEARNING Tolman, E. C. (1953). Edward Tolman and cognitive maps. Douglas Mook (2004), Classic experiments in psychology (pp. 139-142). Westport, Greenwood Press. Vestor, F. (1998). Die Deutsche Schule, 93(2), 186-198. Retrieved from http://www. oecd. org/edu/ceri/34926352. pdf 16 MAZE LEARNING 17 Appendix A: Maze A & B MAZE LEARNING Appendix A 18 MAZE LEARNING 19

Book Report on the Blind Side Essay

The Blind side The Blind Side directed by John Lee Hancock was a visual text about a teenage boy named Michael. Based on a true story Michael, nicknamed Big Mike has grown up in a poor and broken family and goes to a public school where no one really cares about him. Growing up this way has left Big Mike emotionally deprived and lonely. Thanks to his Friend’s dad Michael gets the opportunity to go to a private school on a scholarship. Suddenly he has teachers that care about him and while his life seems to be slowly improving, Big Mike still uses other people’s washing machines in the Laundromat, does not sleep at home and stays at the gym at school because it was warm. The biggest turning point in this movie was when Leigh Anne Touhy sees Big Mike on the side of the road and lets Big Mike have a place to stay. Leigh is a woman that gets what she wants and it is clear from the moment she meets Mike that she would care for him. From this point Big Mike and Leigh build a strong relation ship, he ends up moving in with them and becomes a part of the family. Michael is a big man and one of the reasons he was accepted into the school was because he had the perfect build to play American football and by the end of the movie Big Mike was one of the top players and went on to have a career in it. My favorite character throughout the book was definitely Big Mike, I love how complex of a character the director made him. Appearance wise, Big Mike looked big and tough, he was the type of boy that you would walk the opposite direction when you see him on the street, but when you see him in the movie you discover how kind hearted he is. A classic example of this is when Big Mike is first playing football and he doesn’t tackle anyone because he doesn’t want to hurt anyone. He reminds me of a giant teddy bear that wouldn’t hurt anyone. But then as well as his kind heart if you dig deeper you can see the inner strength he possesses. From a very young age Michael is forced to look after himself and to get through it the way he did could only be done with utter strength. When most people are left with no one they give up but I admire Big Mike so much for turning to himself and doing all he could to make his life work. Not only is this but his loyalty unbreakable. To get Big Mike to tackle at the practice Leigh said to him to pretend that these guys were going to hurt her and his family and that’s when he finally tackled with aggression. You could see then and there that Big Mike would take on anyone that tried to hurt his family and those he cared about. To me it Big Mike is, for lack of a better expression, a total cutie. My favorite part of the movie is when Leigh asks Big Mike if he would like to be part of their family and Big Mike looks at her dead seriously and replies ‘I thought I already was.’ Throughout the whole movie it was this character that constantly impressed and engaged me and the fact that it was based on a true story just adds to this. One of the main ideas in the visual text The Blind Side is courage. Leigh Touhy shows courage when she takes Mike Oher from off the streets and gives him a roof over his head and someone to lean on. This showed courage in the best of ways and it couldn’t off been done to anyone else. Although Leigh’s family did not agree with having Mike there in the first place, then soon got to like the guy and really enjoyed having him there as another brother or son. It also took real courage for Leigh and Michael to legally adopt Big Mike as a child, get his driver license and help him get into the best school available for Mike to go to on a football scholarship. Leigh also had courage for going to her own friends and telling them about Mike. A conversation held with her friends is. Friend: â€Å"You’re changing that boy’s life† Leigh: â€Å"No He’s changing mine†. I thought that Leigh had courage to say this to her friends as Mike is not her own son yet she is taking care of him as he is the only child in the family. A quote from the film The Blind Side to represent Courage is â€Å"that’s why courage is tricky. Should you always do what others tell you to do? Sometimes you might not even know why you’re doing something. I mean, any fool can have courage†. This is saying that courage is important but it’s hard. You should do what you want to do and not what others tell you to do,  but the main point is that anyone can have courage; weather their big, small, tall or short. The text that I immediately thought of was The Dead Poets society and in particular Neil. The reason for this is in my mind I started to immediately compare the difference between Neil and Michael. As I previously stated Big Mike had to deal with the loneliness in his life and the way he did this was by turning to himself for support. I think the reason that Neil committed suicide was loneliness, by this I don’t mean that he had no friends, as it was obvious from the start he did, but that he felt like he had no support from those that mattered. If his dad had shown a slight interest in his acting career then Neil would have been satisfied but because his dad seemed not to care Neil felt like he had no one to turn to and no options. This is the difference that I see between Neil and Michael, inner strength. While Michael appeared soft throughout the visual text, to carry on living especially in certain points in his life took incredible inner strength and as much as I liked Ne il’s character I don’t think he possessed the same strength. Neil is kind of the polar opposite, on the outside he appeared to be strong and content with life but on the inside the way his father was acting slowly killed him inside. Both of these characters had parents that weren’t at all good at their job but it was the difference between the two personalities that ended with one dead and the other a professional football player.

Critical Description of J.S. Bachs Prelude no. 12 essays

Critical Description of J.S. Bach's Prelude no. 12 essays This piece is taken from Book 2 of J.S. Bachs Forty-Eight Preludes and Fugues (also known as The Well-Tempered Clavier). A prelude could take almost any form, the only conditions being that it should be in the same key as the fugue and form a suitable preparation of the listeners ear and mind for what is to follow, although Bachs preludes were usually a clearly defined musical personality, of which the fugues were logical developments and projections. Prelude no XII is in F minor. Pieces in a minor key are often less cheerful and perhaps darker than those in a major key, and while this prelude is not at all gloomy or dismal, it is somehow quite reflective. The listener does not simply a receive a happy four-minute ditty that is forgotten the moment after the recording finishes (as could be said for some classical pieces that I have heard); it is much more thought-provoking than that. The prelude, and indeed the entire work from which it originates, was designed for a keyboard soloist and from the recording I can well imagine the soloist, even Bach himself playing with great feeling and emotion. This is typically what the audience likes to hear from solo performances, unlike huge orchestras where an individuals efforts can be drowned out by a mass of horns and strings. That is probably why the piece is best suited to the piano rather than any other instrument, such as a violin. Often when I hear violins I expect them to be part of a larger string section, or at least supported by a section. I imagine, perhaps somewhat ignorantly that violins are great for playing fast and furiously, or slowly and serenely, but not for the mid-tempo, middle ground. The piano, however, can achieve this. The performer is instructed to play this piece allegretto espressivo. The listener wants to be able to envisage the pianist playing from the heart, and I think that this performer achieves that. ...

Writing for Your Audience

Writing for Your Audience Writing for Your Audience Writing for Your Audience By Erin Im an editor and moderator at Toasted Cheese, a literary magazine and writing community. Recently, one of our members posted a question that I thought was worth addressing here. Hed turned in a college paper, and his professor told him he needed to create more distance from the reader. It all comes down, I think, to keeping your intended audience in mind. In my college writing class, I teach my students to adjust their style according to the assignment. In a personal narrative, for example, an informal tone is welcome. In a research paper, however, that same informal tone can work against the writer. Here are a few general tips: Reserve first person for informal writing like personal narratives, blogs, editorials and columns, and of course, fiction. Avoid addressing the reader (you) and speaking for the reader (we/us), except in informal writing. Both practices run the risk of alienating the reader. Avoid contractions and slang. Ive actually had students who have used curse words and colloquial expressions (bros before hos) in papers theyve turned in to me! Unless it serves a clear purpose, its not going to impress anyone. Be specific, and dont include unsubstantiated claims in formal papers. Research papers need evidence and quotations to back up the authors thesis. Before you begin any piece of writing, ask yourself three questions: What is my purpose? (What do I hope to accomplish with this piece?) Who is my audience? (Who am I writing this for?) And finally, what is the appropriate tone for the writing Im doing? (Formal? Informal? Humorous? Serious?) If you can answer those questions, youll be well on your way to writing appropriately for your audience. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Writing Basics category, check our popular posts, or choose a related post below:50 Slang Terms for Money75 Synonyms for â€Å"Talk†Types of Plots

Marketing Research Essay Example | Topics and Well Written Essays - 3000 words

Marketing Research - Essay Example With all of the important steps the research is designed and done accordingly to fetch the ultimate outcome. Introduction: Market forecasting is an important factor to be analyzed by the marketing team of the organization. For any decision the marketing research is very important. Starting from the customer satisfaction to the new product development and new branding strategies; the marketing research is important in all the aspects of marketing. This paper has different chapters dedicated to the thorough study of the marketing research. The importance of the marketing research in the decision making process, the different methodologies and data collection techniques are discussed thoroughly in this particular paper. The aim of this study is to understand the importance of the marketing research in the field of marketing decision making processes and forecasting. The Importance of the marketing research: The marketing research is the specific marketing function which is conducted to get the ultimate support for taking the marketing decisions (Wrenn, Stevens and Loudon, 2006). According to the American Marketing Association the marketing is defined as â€Å"the function which links the consumers, customer, and public to the marketer through information† (Wrenn, Stevens and Loudon, 2006). The marketing research is possible with the specified data, and it is done for some specific reason. It is a very expensive marketing affair. However, the best marketing research does not promise to produce the best marketing decision always. The marketing research specifies the important information to be needed to analyze the situation within and outside the organization. Without the marketing research no product development is possible. The proper marketing research tells the organization what are required to meet the expectations from the market. This is an essential function within the marketing department to simplify the future decision towards the development. Mark eting research is the ultimate option to understand the internal strength of the organizations and also the expected performance from the external environment. This is the quantitative analysis which would fetch the ultimate solutions to the specified problems. The mathematical and the statistical approaches help the marketing research to have the measurable characteristics. Role of marketing research in decision making: One of the main role of the marketing research is to simplify the decision making process in an efficient way. However, the complete marketing research plays two major role in the whole marketing system, and they are; 1. They are the part of the marketing intelligence feedback function, and 2. It provides the ultimate quantitative data to the decision makers to take decision accordingly towards future advancement. The segmentation research and the new product research are the most lucrative field in the marketing for the opportunist marketing managers (McDaniel and Gates, 1998). From customer satisfaction to the brand extension, every step is taken carefully with the suitable marketing research programs by most of the organizations. Satisfying customers is the main motive of most of the organizations in the recent business environment. And, to work according to