# Is there any relationship between IQ and Sat Results?

Maths Coursework

The aim of this piece of coursework is to test these two hypotheses:

1. Is there any relationship between IQ and Sat Results?
2. Is there a difference between the development of IQ over time between boys and girls?

To do this I will use the data collected from Mayfair High School. To test that my hypotheses were not too difficult to test and gave an outcome that I could show had correlation, I did a preliminary graph. This consisted of random Sat Results and IQ’s taken from year 7 girls and boys. These graphs both came out with correlations, and so I proceeded with these hypotheses.

There was a lot of data available, not all of which was useful to my study, and therefore I deleted any information I considered to be irrelevant, like height and weight of each of the people. I then ended up with just the relevant data I needed, which is:

• Year Group
• Gender
• IQ
• Sat Results

I then decided to do a stratified sample, using 10% of my entire database. I did this because 10% of my entire data range will give me enough results to form a conclusion, and will also keep the numbers manageable. Using a stratified sample also ensured that I got the same proportions of each year group and the different genders, as in the entire database. Hence I proceeded to work out the proportions needed in my stratified sample as such:

I decided to round any values I got in decimal form up if it was or was over .5. I realises this introduces bias but seemed more logical, fair and conclusive method.

After working out these values I then put this into affect in my data. To ensure fairness during my test I assigned each piece of data a random number using Microsoft Excel. Then I sorted the data according to their random numbers, highest at the top, and preceded to pick the set of numbers I needed for my stratified sample, taking them from the top until I had all I needed. When stratifying my data I came about some problems, which I will discuss later.

To see if there indeed was a correlation between Sat Results and IQ, I decided to plot graphs. I plotted two graphs for each year group, both of different gender. I also used box plots to show my data, doing them the same as the graphs.

This is the result of the graphs:

## YEAR 7

Female:

In this graph we clearly see a relatively weak correlation between the IQ of the young girls and their KS3 Sat Results. It doesn’t really matter about their IQ; as they’re all quite close together anyhow, and still they're marks still have quite ...