# 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∑d²

n(n²-1)

Spearman’s Rank = 1 - 6∑d²

20(20²-1)

Spearman’s Rank = 1 - 6∑d²

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∑d²

n(n²-1)

Spearman’s Rank = 1 - 6∑d²

19(19²-1)

Spearman’s Rank = 1 - 6∑d²

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.

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

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