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The higher the IQ, the higher the average SATs results

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Statistics Coursework


1. The higher the IQ, the higher the average SATs results. There will be a stronger relationship between the girls’ IQ and SATs results than the boys’.

2. Boys will have a higher IQ than girls.

3. IQ will increase as age increases.


I have been given two sheets of containing 100 pieces of data on each. The data is secondary as I have not collected it myself. One set is from key stage three and the other from key stage four. The data includes year group, forename, age, gender, hair colour, eye colour, favourite type of music, IQ, height, weight, distance between home and school and SATs results.

I will use a sample of 80 students, because 200 is too time consuming. A sample of 80 will still give me a reliable answer. I will use a stratified sample so my sample is in proportion as the full set of data.

To do the stratified sample I am going to count how many year seven, eight, nine, ten and eleven students there are on the sheets of data. I will then divide the total number of year seven students by the total number of pupils, then times by 80. I will repeat this for the remaining year groups to complete my stratified sample.

...read more.


I will use the fencing method to calculate outliers. This is where I will multiply the inter-quartile range by 1.5, then, subtract this from the lower quartile. Any values lower than the smallest value are outliers at the bottom end. To find the outliers at the top end I will multiply the IQR by 1.5 and then add this answer to the upper quartile. Anything above the highest value are outliers.

Hypothesis 3

IQ increases as age increases

To prove this hypothesis I will put my data in to five separate boxplots. One for year seven, one for year eight, one for year nine, one for year ten and one for year eleven.

I will use these boxplots to compare IQ scores of different age groups.

I will use the fencing method to calculate any outliers.

I will expect the scores to higher in general for year eleven.

Stratified Sample

Year Seven: (30/200) × 80 = 12

Year Eight: (38/200) × 80 = 15

Year Nine: (32/200) × 80 = 13

Year Ten: (53/200) × 80 = 21

Year Eleven: (47/200) × 80 = 19

Results Interpretation

Hypothesis 1

The higher the IQ, the higher the average SATs results. There will be a stronger relationship between the girls’ IQ and average SATs results than the boys’.

The correlation for all the data is a positive one (0.7489830411). This has proved the first part of my hypothesis correct.

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In the year ten boxplot the difference between the lower and upper quartile is 21, the LQ is 92 and the UQ is 113. The lowest value is substantially lower. It is 76, where as all the others are around 83. The lower quartile is similar to year nine. Once again the medians are the same. The UQ in year ten is 113, much larger than the others. The highest value is between the two highest values for year eight and nine.

As I mentioned earlier the values in the year eleven boxplot are larger. The LQ is about the same as all the other medians, the median is higher than most of the other upper quartiles and the UQ is larger than all the others. The highest value is 125, this is the higher than all the others by at least 4.


Generally, my coursework went quite easily. I didn’t encounter any problems apart from entering data in to a graphical calculator. I had to repeat this process a number of times due to missing out data.

If I were to repeat the coursework I would use a larger sample size or compare data from different schools to make sure my results are correct for the country or just a few schools in particular.

...read more.

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