# Maths Coursework on IQ

Maths Coursework

Statistics

Year 10

Mayfield High School

Lucy Andrews

11SRH

SET 2

## Intoduction

My aim is to investigate the relationship between the IQ and Key Stage results of a group of students.  I will show if there is any correlation between;

IQ and Key Stage Results in years 7, 8 and 9

If I find an outlier in any of my graphs, I will try and explain why it is there and see if my line of best fit fits better without it.

I will now conduct a pre-trial to test if there are, in fact, any of there correlations;

MASOOMA ABBAS                (male)                IQ – 101

KS2 – Eng-3                Maths-4                Sci-4

ZAHARA ABBOTT                (female)        IQ – 116

KS2 – Eng-5                Maths-5                Sci-5

As you can see from the graphs on the previous page, there is some evidence of a correlation between the IQ and the KS2 results.  This is highlighted by Zahara’s IQ being noticeably higher than Masooma’s.  So too are her Key Stage 2 results.  I can conclude therefore that there is reason for me to continue with my tests.  The findings of the pre-test suggest a possible correlation between the IQ and Key Stage 2 results of these particular students and therefore makes my project worthwhile.

Throughout this coursework, I will be using stratified sampling.  In order to do this, I will divide the population into groups which have something in common.  Simple random samples will then be taken from each group.  The number taken from each group must be proportional to the size of the group.  This is a useful form of sampling as it is relatively simple and is often used to represent more complex populations.  A disadvantage of this sort of sampling is that I may get “clumps” of data, but I will try and avoid this.

Another problem I must investigate is that of age.  The separation age of the school years (how to determine which year a student should be in), is September 1st.  If one boy is born in late August and another in early September (excluding September 1st), and the latter is therefore older, the IQ is likely to be higher for the older boy than for the younger one.  This is because up to the age of 16, your IQ is constantly growing as the individual grows.  This is a problem for my project, as the correlation will not be as strong between these boys and outliers may be created.  For example, Wasim Ahmed was born in October and is 12 years of age and Mark Anderson was born in May and is only 11 years old, but the two are still in the same academic year.  This is not an extreme example and yet there are many of them in the data.

My objectives for this coursework are generally to find a strong positive correlation between the IQ and Key Stage results of the children in all the academic years.  I will be able to note if the correlation between these two has become more or less of a positive correlation between the years, as well as checking if the IQ and Key Stage results as an average have changed.  By doing this I can also see if, as the years have gone by, children have become more or less intelligent.  I will be able to identify if the average IQ and Key Stage results changes between boys and girls.  I believe that overall boys will not perform as well as girls.  This is because, in general, boys are said to under perform, whereas girls are possibly more focused on their work and therefore work to a higher standard at this point in their education. Also girls mature earlier than boys which could indicate that girls want to work harder

I believe that there will be a highly positive correlation between the IQ and Key Stage 2 results; this is probable as it would make sense that if a child is generally bright, they are likely to get high KS2 results.

I must now sample my data into groups and then “simple random sample” these groups to accumulate the data that I will then be using throughout my processing.

The groups will be divided by academic year groups.  Listed below are the numbers of girls and ...