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• Level: GCSE
• Subject: Maths
• Word count: 2224

# Using the data from Mayfield High School, I am going to be investigating the relationship between IQ level and Key Stage 2 results.

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Introduction

Using the data from Mayfield High School, I am going to be investigating the relationship between IQ level and Key Stage 2 results. I would expect to find that people with higher IQ will have higher KS2 results. I am going to take a random stratified sample of 60 students; this will enable me to take a proportional amount of pupils from each year group. To do this calculation I needed to find the number of people in each year group then divide it by the total number of people in the school, after you have done this you need to multiply it by the size of your stratified sample.

So my calculation for the number of students I need from year 7 would be: 282/1183*60=14.3… as this is a decimal answer I will have to round it off to the nearest whole number. As mine is 14.3 I will round it own to 14.

 Year Calculation Number of Pupils 7 (282/1183) x 60 14 8 (270/1183) x 60 14 9 (261/1183) x 60 13 10 (200/1183) x 60 10 11 (170/1183) x 60 9 60

This table shows me how many pupils I need from each year group. To start off with I gave each student a number from 1 – 1183, I then sorted the data into year groups and then I generated a random number between 1 –1183 using my calculator.

In order to see if there is any relationship between Key Stage 2 results and IQ I am going to draw scatter diagrams.

Middle

11

110

4.6

11

102

4.3

11

101

3.3

11

109

4.3

11

92

3.3

11

104

4.3

11

103

4

11

99

4.3

I will now find the averages for IQ and KS2 for each year then the entire school.

## Averages… IQ…

To get the average IQ I added up all the IQ’s in the certain year and then divided the total by the number of students in my sample in that year.

Year 7 = 1416 / 14 = 101.1

Year 8 = 1416 / 14 = 101.1

Year 9 = 1291 / 13 = 99.3

Year 10 = 1004 / 10 = 100.4

Year 11 = 930 / 9 = 103.3

All years = 6057 / 60 = 100.95

This is the average IQ for the entire school.

## Average KS2

I got the average Key Stage 2 results by adding up each students key stage 2 results then divided each students total KS2 results by 3, this enabled me to find the average of each child. To get the year average I added up all the children’s average KS2 results then divided it by the number of students in the year’s sample.

Year 7 = 58.2 / 14 = 4.15

Year 8 = 58 / 14 = 4.14

Year 9 = 49.9 / 13 = 3.83

Year 10 = 39.1 / 10 = 3.91

Year 11 = 36.8 / 10 = 3.68

All years = 24.2 / 60 = 4.03

These results are quite interesting, as the year’s progress it seems people are getting higher key stage 2 results. This could be due to many influential factors: the method in which the teachers teach their students may have improved. Another factor could be that the parents encourage their children to study more at home, so this in turn will help the students improve their grades.

Analysis of Scatter Diagrams…

After completing my year 7 scatter diagram I have noticed that there is a strong positive correlation. My line of best fit shows this. I have drawn a line of best fit so that I will be able to predict someone’s IQ level from his or her average Key Stage 2 results and vice-versa. Most the points were close to the line apart from 2 odd points; one of the points is quite far below the line of best fit, while the other is very far above the line of best fit.

In Year 8 the same sort of trend followed from year 7 but there was not as a strong correlation as before. This could be due to my hypothesis, which I made earlier.

In year 9 the trend continued but there was one extreme point, which was very far away from the line of best fit. This was the only extreme point but there were other points, which were quite far away from the line of best fit. 5 points all resided on the same x-axis, which was 4. So that must mean that quite a number of people got a key stage 2 average of 4

In year 10 the trend stayed the same but the points were not as closely packed, as before, there was gaps between them. The majority of the points resided higher on the line of best fit only 3 points were below an average key stage 2 result of 4.

In year 11 there were no unusual points, all the points stayed close to the line of best fit.

After looking at my statistics it is clear that there is a slight relationship to the IQ and Key Stage 2 results. This does not mean that body with the same IQ got the same key stage 2 results or vice versa.  Using my lines of best fit I am able to predict the IQ of a person with the average key stage 2 result of 4.6. I obtained the following results:

 Year Average Key Stage 2 Result IQ 7 4.6 106 8 4.6 103 9 4.6 103 10 4.6 108 11 4.6 108

Conclusion

Cumulative Frequency…

Year 7

 IQ Tally Frequency Cumulative Frequency 70

Year 8

 IQ Tally Frequency Cumulative Frequency 70

Year 9

 IQ Tally Frequency Cumulative Frequency 60

Year 10

 IQ Tally Frequency Cumulative Frequency 60

Year 11

 IQ Tally Frequency Cumulative Frequency 60

## Summary of cumulative frequency results for IQ

 Year Median Lower Quartile Upper Quartile Inter Quartile Range 7 7 3.5 10.5 7 8 7 3.5 10.5 7 9 6.5 3.25 9.75 6.5 10 5 2.5 7.5 5 11 4.5 2.25 6.75 4.5

The table shows that most of the data from the year 7 and 8 lies within a larger spread of the median value. This could mean that year 7’s and 8 have a varying IQ level more than any other year group. This statement backs up my hypothesis previously. This information also suggests that year 11 fall within a more closely packed inter quartile range.

After all my research I found out that the older the students the worse key stage 2 results they had. So for example a when a current year 7 becomes a year 11 that student will have worse results than a new year 7.

This student written piece of work is one of many that can be found in our GCSE IQ Correlation section.

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