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# Investigate the hypothesis that the in KS3 the higher your IQ is, the higher your average Key Stage results is.

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Introduction

Hypothesis Here in this statistical piece of course work we are given a spreadsheet with loads of information about students in Mayfield High. This spreadsheet was provided to us by the school. Below are the headings that are available on the spreadsheet. * Name * Age * School year * Hair colour * Eye colour * Favorite colour * Favorite sport * Favorite Subject * Favorite TV program * Number of TV hours per week * IQ * Height & Weight * Distance from school * Means of transport to school * No. of siblings * No. of pets * KS2 results (English, math, Science) Specify the Problem and Plan For my statistics assignment I am going to investigate the hypothesis that the in KS3 the higher your IQ is, the higher your average Key Stage results is. So if a student has a high IQ he'd have a high key stage results but if he has a low IQ he'd have a low Key Stage results. And that Female's have a higher IQ and do better than males in their KS3 results. I think this is true because IQ is a representation of the human smartness and that would affect greatly the average results. * Student ID (I have created that for later sampling use) * Year Group * Gender * IQ * KS3 Math's results * KS3 Science Results * KS3 English Results * Average KS3 Result I will get this information from a spreadsheet given to us. I will use all the years 10 & 11. ...read more.

Middle

22 94 10 3.3 9.5 0.5 0.25 23 88 2.5 3.3 9.5 -7 49 24 108 42 4.7 42 0 0 25 94 10 3.3 9.5 0.5 0.25 26 116 47.5 5.0 46.5 1 1 27 100 19.5 4.0 25 -5.5 30.25 28 103 29 4.0 25 4 16 29 101 22.5 4.3 36.5 -14 196 30 88 2.5 3.0 2.5 0 0 31 103 29 4.3 36.5 -7.5 56.25 32 106 36.5 4.0 25 11.5 132.25 33 104 33 4.3 36.5 -3.5 12.25 34 97 14 3.7 15.5 -1.5 2.25 35 105 35 4.0 25 10 100 36 107 39 4.0 25 14 196 37 102 24.5 4.0 25 -0.5 0.25 38 113 45.5 5.0 46.5 -1 1 39 90 4 3.0 2.5 1.5 2.25 40 113 45.5 4.0 25 20.5 420.25 41 121 50 5.0 46.5 3.5 12.25 42 108 42 4.0 25 17 289 43 98 15 3.3 9.5 5.5 30.25 44 107 39 5.0 46.5 -7.5 56.25 45 118 49 5.0 46.5 2.5 6.25 46 104 33 4.3 36.5 -3.5 12.25 47 99 16.5 3.7 15.5 1 1 48 111 44 5.3 50 -6 36 49 108 42 5.0 46.5 -4.5 20.25 50 96 13 3.7 15.5 -2.5 6.25 ? = 2421.25 To find Spearman's Rank I will have to use this expression This equation lets us multiply the number of pairs (n) times the square of the number of pairs minus 1, to divide this quantity into the number obtained by multiplying 6 times Rank Difference2, and to subtract the result from 1. ...read more.

Conclusion

Number x x - x ( x - x )� 1 2 -1.70833 2.918403 2 3 -0.70833 0.501736 3 3 -0.70833 0.501736 4 3 -0.70833 0.501736 5 3 -0.70833 0.501736 6 3 -0.70833 0.501736 7 4 0.291667 0.085069 8 4 0.291667 0.085069 9 3 -0.70833 0.501736 10 3 -0.70833 0.501736 11 4 0.291667 0.085069 12 4 0.291667 0.085069 13 4 0.291667 0.085069 14 4 0.291667 0.085069 15 4 0.291667 0.085069 16 4 0.291667 0.085069 17 4 0.291667 0.085069 18 4 0.291667 0.085069 19 4 0.291667 0.085069 20 4 0.291667 0.085069 21 5 1.291667 1.668403 22 4 0.291667 0.085069 23 5 1.291667 1.668403 24 4 0.291667 0.085069 3.708333 0.456597 0.67572 Standard Deviation Value MEAN ? As you can see the standard deviation of the males is 0.750739 and the one for females is 0.67572 this supports my hypothesis as it shows that the females results are more accumulated around the mean than the males. The smaller the standard deviation when compared to the other one shows that the results surrounding the mean are closely accumulated. I am happy with all my conclusions and results as I have firstly used a fair sampling method which gave me a sample which was random. Secondly I'm happy with my calculations because I have done every one of them at least twice extra to the ones shown so that I would have missed anything out or made any mistake in calculations. I also am happy with the reliability as they have all supported my hypotheses. And lastly I am sure that my results are reliable because I have a firm understanding of all the methods used. Khalid Abu Rumman, Khalid Abu Rumman GCSE Mathematics Mr. Mc Inerny 11s Statistics Coursework - 1 - ...read more.

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