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• Level: GCSE
• Subject: Maths
• Word count: 2796

# IQ Investigation

Extracts from this document...

Introduction

Natalie Mansell                Mayfield High Maths Coursework

Mayfield High Maths

Coursework

I am investigating around data about a school called Mayfield High. Mayfield High is a database of secondary data and I will be using only the Key Stage 3 pieces of data. I am doing this investigation so that I can find links between different aspects of secondary school pupils, and create charts and graphs to show the patterns that I have found.

I am going to look at a database on excel. I will then take a stratified sample of years 7, 8 and 9, depending on my sample size I have chosen to be 60 (because I think that it is a viable size).

After I have worked out my stratified sample I will give each member of each year group a unique number and use random number tables to choose my final sample so that my sample is an unbiased one, giving no special interest to any specific data in particular.

I believe that the more people watch TV, the lower their IQ should be. I also believe that the further people go up the school, the higher their IQ should be and that girls are generally cleverer than boys throughout Key Stage 3. I also believe that there may be a relationship between people’s IQ and the amount of time they watch TV and that the relationship between IQ and TV shows a higher correlation as you move up the school.

Middle

97

17

17

6

11

121

∑ = 1597

Spearman’s Rank = 1 - 6

n(n²-1)

Spearman’s Rank = 1 - 6

20(20²-1)

Spearman’s Rank = 1 - 6

7980

Spearman’s Rank = 1 – 9582

7980

Spearman’s Rank = 1 – 1.2

Spearman’s Rank = - 0.2. Similar to year 7, this also shows a very weak correlation between the two areas, IQ and amount of time spent watching TV. This also adds to my scatter diagram analysis, as this year 8 sample proves to have a higher correlation than the year 7 sample. This now adds to my hypothesis, as it proves there may be a possibility that the correlation between TV and IQ becomes greater as you get older.

YEAR 9

 IQ Average No. of hours spent watching T.V. Spearman’s Rank Hours Rank D (S Rank – H Rank) D² 106 4 6 17 -11 121 108 10 4 13 -9 81 107 7 5 15 -10 100 112 4 2 17 -15 225 102 14 11 7 4 16 92 42 14 1 13 169 69 25 19 3 16 256 101 3 12 19 -7 49 78 21 18 5 13 169 103 14 9 7 2 4 88 11 16 11 5 25 120 8 1 14 -13 169 90 12 15 10 5 25 104 42 7 1 6 36 79 14 17 7 10 100 97 24 13 4 9 81 104 6 7 16 -9 81 103 10.5 9 12 -3 9 110 16 3 6 -3 9

∑ = 1531

Spearman’s Rank = 1 - 6

n(n²-1)

Spearman’s Rank = 1 - 6

19(19²-1)

Spearman’s Rank = 1 - 6

6840

Spearman’s Rank = 1 – 9186

6840

Spearman’s Rank = 0.34. This shows a reasonable correlation between IQ and TV in year 9 pupils. This backs up my scatter diagram analysis and proves my hypothesis that the relationship between the 2 areas gets stronger as you move up the school.

For each set of information for years 7, 8 and 9 I then totalled all of the pieces of data and divided by the number of pieces to get the mean. All means are to 1 decimal place. I will now use the tables to perform standard deviation for each year group on Amount of time spent watching TV to find out how spread out the data is.

YEAR 7

 MALES FEMALES Number Average hours spent watching T.V. IQ Average hours spent watching T.V. IQ 1 7 109 12 94 2 20 101 13 106 3 8 72 14 110 4 50 107 18 113 5 12 103 10 103 6 23 108 14 101 7 20 74 21 84 8 14 96 18 116 9 6 100 24 100 10 11 97 25 108 11 7 100 ∑ 171 967 176 1135 MEAN 17.1 96.7 16.0 103.2

YEAR 8

 MALES FEMALES Number Average hours spent watching T.V. IQ Average hours spent watching T.V. IQ 1 15 103 18 99 2 25 97 28 102 3 10 100 10 100 4 7 112 7 114 5 2 114 13 94 6 9 101 12 109 7 15 117 14 87 8 15 107 14 101 9 19 126 10 8 100 11 21 106 12 17 97 ∑ 163 1280 116 806 MEAN 13.6 106.7 14.5 100.8

Conclusion

 MALES Average hours spent watching T.V. X - mean (X – mean)² 15 1.4 1.96 25 11.4 129.96 10 - 3.6 12.96 7 - 6.6 43.56 2 - 11.6 134.56 9 - 4.6 21.16 15 1.4 1.96 15 1.4 1.96 19 5.4 29.16 8 - 5.6 31.36 21 7.4 54.76 17 3.4 11.56 163 (total) 474.92 13.6 (mean)
 FEMALES Average hours spent watching T.V. X - mean (X – mean)² 18 3.5 12.25 28 13.5 182.25 10 - 4.5 20.25 7 - 7.5 56.25 13 - 1.5 2.25 12 - 2.5 6.25 14 - 0.5 0.25 14 - 0.5 0.25 116 (total) 280 14.5 (mean)

This standard deviation has shown me a value higher for year 8 males than year 8 females, disproving my analysis of my histogram for the sample I chose. (The higher the standard deviation the more spread out the data is). So, in all 3 year groups the data is more spread out and varied in males than in females.

In this investigation I have found out that in years 7, 8 and 9 the IQ is more spread out for males and that the females’ IQs are closer together. I have also found that there is no strong correlation in either of the 3 year groups between Amount of time spent watching TV and IQ. I have found that generally in years 7, 8 and 9 girls are more intelligent than boys. I disproved one of my hypotheses because I found that there was no great correlation between IQ and TV in any year group. I proved another of my hypotheses in that I found girls were generally more intelligent than boys throughout Key Stage 3. Overall, some of my hypotheses were proven in this investigation, and some were not – but they were all either proven or unproven by my statistical analysis.

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