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

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.

As

From Table 1:                            

1. 2
2. 8
3. 6
4. 11

From Table 2:

1. 4
2. 5
3. 9

From Table 3:

1. 6
2. 10
3. 2
4. 20
5. 8
6. 22
7. 17
8. 5

From table 4:

1. 16
2. 5
3. 6
4. 10
5. 4
6. 14
7. 9

From Table 5:

1. 6
2. 21
3. 14
4. 7
5. 17
6. 12
7. 11
8. 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.

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.