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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.

...read more.

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)

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

...read more.

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.

                

...read more.

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