# Mathematics coursework

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Introduction

## Mathematics coursework

## Introduction

Al the way through my coursework I will be exploring the positive and negative correlation between IQ scores and exam results in The Swaminarayan Independent day school. I also used data provided by Edexcel on the KS2 results and the IQ results in the Mayfield School. I will be carrying out investigation to see whether the IQ results have any significance towards how a student performs in his exams.

## Mayfield Data

IQ |

89 |

103 |

98 |

108 |

94 |

91 |

116 |

104 |

103 |

90 |

97 |

116 |

94 |

113 |

106 |

95 |

105 |

101 |

Total KS2 results |

9 |

13 |

9 |

15 |

10 |

11 |

15 |

13 |

13 |

12 |

10 |

15 |

10 |

12 |

13 |

12 |

13 |

12 |

As you can see above, there are the first 30 IQ results by the Mayfield data. I will now try and prove that there is some kind for correlation between these two sets of data above. I will create a scatter graph in the Edexcel programme.

As you see above, there is a positive correlation between the IQ scores and the total KS2 results. Now I will see whether there is correlation between the IQ scores and the English scores.

IQ | English |

89 | 3 |

103 | 4 |

98 | 3 |

108 | 5 |

94 | 3 |

91 | 4 |

116 | 5 |

104 | 4 |

103 | 5 |

90 | 4 |

97 | 2 |

116 | 5 |

94 | 4 |

113 | 4 |

106 | 5 |

95 | 4 |

105 | 4 |

101 | 4 |

As

Middle

From Table 1:

- 2
- 8
- 6
- 11

From Table 2:

- 4
- 5
- 9

From Table 3:

- 6
- 10
- 2
- 20
- 8
- 22
- 17
- 5

From table 4:

- 16
- 5
- 6
- 10
- 4
- 14
- 9

From Table 5:

- 6
- 21
- 14
- 7
- 17
- 12
- 11
- 4

Proving My Hypothesis.

Because everything has been decided I shall now make a scatter graph to prove my hypothesis. I will distinguish whether there is a correlation and then use the Spearman’s Rho Theorem to learn the strength of the correlation.

As seen above there is positive correlation between the Maths results and the CAT results.

I will know learn the strength of the two positive by using the Spearman’s Rho Theorem.

Spearman’s Rho Theorem

I will be explaining the method in steps to ensure clarity.

Conclusion

Step 3

I will now have to count the number of paired scores. In this case the number of paired scores is 30. So N=30.

Step 4

I will now multiply N by it’s own value, twice, then subtract it’s own value.

(30*30*30)-30 =27000-30=26970.

Step 5

I shall now total all the values in the column D2.

49+110.25+1+20.25+12.25+0.25+4+42.25+6.25+6.25+64+1+100+30.25+272.25+49+1+1+625+1+0+2.25+36+81+16+81+225+20.25=

1872.25

Step 6

I will now multiply the value I obtained in step 5 by 6; then divide the result by the value I found in step 4.

1872.25*6 = 11233.5 =0.4165 to four d.p

26970 26970

Step 7

I shall now find Rho by subtracting the number I obtained in step 6 from 1.

1-0.4165=0.5835

Step 8

My Rho number has exceeded all of the numbers below:

0.306

0.364

0.432

0.478

My Conclusion

I am going to end my coursework by expressing how I would improve on my hypothesis should the opportunity to repeat it arise. I may use a bigger population or maybe use different methods to randomize numbers. I am glad that my hypothesis didn’t turn out to be a null one. From this investigation I have learnt a lot about statistics and would jump at the opportunity to learn more about the topic.

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

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