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  • Level: GCSE
  • Subject: Maths
  • Word count: 9664

Mayfield High School

Extracts from this document...

Introduction

Introduction

I have chosen to compare the relationship between IQ and Key Stage 2 Results and my hypothesis is that the greater the person’s IQ, the better their Key Stage 2 will be. I will use scatter graphs to represent my data and to find out if my hypothesis is true. For the scatter graphs I will be drawing the lines of best fit, finding the equations of these lines and using this to compare. I will also be using cumulative frequencies and box and whisker diagrams to look at the interquartile range and the median. If my hypothesis is true, I expect to see a positive correlation.  

Sampling the Database

For my whole database I will use stratified samples, where the samples reflect the proportions of the whole population. Therefore, the school is growing and there are more students in year 7 than year 11. This means, there are likely to be more year 7 students in the sample than year 11 students. To ensure that students from different age groups are equally represented my need to take this type of my sample. In a stratified sample my sample values from a particular group in proportion to that group's size within the whole population.

An example of a stratified sample in connection to Mayfield High School is shown below.

For example, I want to make a population of 60 from the population of 1183 shown below from Mayfield High School.

Year Group

Number Of Boys

Number Of Girls

Total

7

151

131

282

8

145

125

270

9

118

143

261

10

106

94

200

11

84

86

170

To get the proportion of any year you would have to do the following:

(Total for Chosen Proportion) ÷ (Overall Total) x (Sample Size)

The answer obtained tells you how many you would need to choose from your chosen proportion, and to choose this you would:

(Total for Chosen Proportion) ÷ Answer

...read more.

Middle

This scatter graph shows female pupils’ IQ and Key Stage 2 Science results. It shows a median positive correlation which therefore means that the greater the IQ, the greater the average Key Stage 2 results are. The R² value relates to the how the average Key Stage 2 results are effected by the IQ. Here we see that the R² is 0.4374 which shows that 44% of the Key Stage 2 Science results are affected by the IQ.  

All these scatter graphs for the female pupils support my hypothesis that the greater the IQ, the greater the Key Stage 2 results will be. Therefore, (as I predicted) you see a positive correlation.

 I have now placed the equations of the line of best fit and the R² values of these scatter graphs into a table.

Equation of line of best fit

IQ/English

Y=0.027x + 1.3621

0.1877

IQ/Maths

Y=0.0499x – 0.9326

0.4017

IQ/Science

Y=0.0521x – 1.1577

0.4374

IQ/Average KS2 Results

Y=0.043x – 0.2428

0.55

By observing the gathered data in the table above, I noticed that the scatter graph showing the Key Stage 2 Science results are affected more by the IQ, than the Maths and English results.

The table also indicates through the R² value, that on average, around 55% of the Key Stage 2 results are affected by the IQ, which shows there is a median relationship between the average Key Stage 2 results and the IQ.

Now I will look at only the Year 7 subset.

Year Group

Years

Gender

IQ

KS2 - English

KS2 - Maths

KS2 - Science

AVERAGE

7

12

Male

106

5

5

4

4.67

7

12

Male

112

5

5

5

5.00

7

12

Male

103

4

5

4

4.33

7

12

Male

100

4

4

4

4.00

7

11

Male

97

3

4

4

3.67

7

12

Male

102

4

4

5

4.33

7

12

Male

103

4

5

5

4.67

7

11

Female

102

4

4

4

4.00

7

12

Female

116

4

4

4

4.00

7

12

Female

88

5

4

3

4.00

7

12

Female

103

4

4

5

4.33

7

12

Female

99

4

4

4

4.00

7

12

Female

106

4

5

5

4.67

AVERAGE

102.85

4.15

4.38

4.31

The following scatter graphs represent data from the Year 7 subset.

image04.png

This is a scatter graph illustrating Year 7 pupils’ IQ and average Key Stage 2 results, with a weak positive correlation, which indicates that the greater the IQ, the greater the average Key Stage 2 results.  The R² value is 0.

...read more.

Conclusion

image31.png

The quadratic equation it is:

Y = -0.0003x² + 0.1134x – 4.4287

If the IQ is 112, then the average Key Stage 2 result would be:

Y = -0.0003x² + 0.1134x – 4.4287

Y = (-0.0003 x 112²) + (0.1134 x 112) – 4.4287

Y = -3.7632 + 12.7008 – 4.4287

Y = 4.5089

However, when the IQ is 112 the actual average Key Stage 2 result is 5; the quadratic equation provided an answer which was 0.4911 less. Therefore, this shows the quadratic equation: Y = -0.0003x² + 0.1134x – 4.4287 is not as accurate as the linear equation.

Now I will investigate the reliability of these results by comparing another linear equation with a quadratic equation, but this time I will use the Key Stage 2 English results and IQ in the sample data from the population of 60.  

image32.png

Here the linear equation is: y = 0.0571x – 1.7348, with y representing the Key Stage 2 English results and x representing the IQ.

If the IQ is 112, then the average Key Stage 2 result would be:

Y = 0.0571x – 1.7348

Y = (0.0571 x 112) – 1.7348

Y = 6.3952 – 1.7348

Y = 4.6604

However, when the IQ is 112 the actual average Key Stage 2 result is 5; the linear equation provided an answer which was 0.3396 less. Therefore, this shows the linear equation: Y = 0.0571x – 1.7348 is quite accurate.

Now I will change the linear equation into a quadratic equation by changing the linear trend line to a polynomial trend line with an order of 2.

image33.png

The quadratic equation it is:

Y = 0.0015x² - 0.2564x + 14.533

If the IQ is 112, then the average Key Stage 2 result would be:

Y = 0.0015x² - 0.2564x + 14.533

Y = (0.0015 x 112²) - (0.2564 x 112) + 14.533

Y = 18.816 - 28.7168 + 14.533

Y = 4.6322

However, when the IQ is 112 the actual average Key Stage 2 result is 5; the quadratic equation provided an answer which was 0.3678 less. Therefore, this shows the quadratic equation: Y = 0.0015x² - 0.2564x + 14.533 is accurate but not as accurate as the linear equation.

Conclusion:

There is a positive correlation between the IQ and KS2 result both across the school as a whole and within each year group. This correlation appears to be stronger when individual year groups and separate genders are considered.

...read more.

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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