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Investigate the correlation between various sets of information from a database of pupils from Mayfield High School.

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Maths Statistics Coursework


In this project I will investigate the correlation between various sets of information from a database of pupils from Mayfield High School. I will try to spot correlation between two different sets of information. I will pick only sets of information that I predict to show good correlation, and therefor tell me something about the data. Example, I will be able to say that girls are more intelligent that boys or vice versa if the correlation shows that to be.


In this investigation I am going to look into the correlation between Key Stage 3 results and IQ test scores of years 10 and 11 pupils, for both boys and girls separately.

Because there is such a large selection of pupils it would be impossible to compare them all, so I took a random selection of 30 pupils. In truth, it isn't really a fully random decision as I have chosen 15 boys and 15 girls. I didn't use a stratified sample because you obviously cannot have 14.7 pupils, and it was so close to 15. To solve this I took a random selection of 50 boys and 50 girls and picked 15 of each from a hat.

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5 - 6



I encountered a problem whilst investigating into cumulative frequency charts and that was that Key Stage 3 results are a discrete form of data. To overcome this I made a mean of the 3 results, English, Science and mathematics. This should give my graphs a better verity of results. I could also try a second table and graph of results using totals of KS3 results instead of means, this would make my graphs easier to decipher.

IQ Scores

Cumulative frequency for boys

Cumulative frequency for girls

















From my cumulative frequency curves I can see positive correlation between KS3 results and IQ scores. As a general trend I can say that the higher the KS3 result the higher the IQ. There is always 'outliers' to the trend, for instance a boy with the mean of 3 at KS3 and an IQ of 103. As a trend I can say that boys have a higher IQ and girls have a higher mean of KS3 results.

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I know that a line of best fit has its limitations, but I can use them to predict a mean KS3 result from any boy with a given IQ. I know that the equation of every straight line is y = mx + c . I must use this to find the equations of my lines of best fit. To do this I must look at the point where they intercept the y axis and find the gradients. ( Y = IQ , X = KS3 )

Boys : Y = 10x + 56

Girls : Y = 8x +68

I will now use this equation to find the result for a boy with an IQ of 102. If Y = 102 then….

102 = 10x + 56


X = 102 - 56


X = 4.6

So a boy with the IQ of 102 should have the mean KS3 result of 4.6, this means that he probably got to 5s and a 4, as 14 ? 3 = 4.6 reoccurring. I can now estimate any IQ from the KS3 mean or vice versa.

Mayfield High School obviously needs to look at the concentration of educational focus between boys and girls, as girls are achieving higher KS3 marks on average. Perhaps if I used a sample of national data I could investigate into the performance of Mayfield High against national means.

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This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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