# Data Analysis Investigation-Higher Tier

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Introduction

By Kyle Harris

Introduction

During this investigation I am going to find out if boys are on average taller than girls and if their average heights are more dispersed.

My hypothesis is:

“On average boys are taller than girls and boy’s heights are more dispersed than girl’s heights.”

Using the data I have been provided by the school I will carry out my investigation. The data provided is based on pupils in our Co-educational comprehensive school. The data has been split up into 5 groups also known as strata; there is one strata for each year group i.e. year 7, 8, 9, 10 and 11. In turn I will look at years 7, 9 and 11 in order to test my hypothesis. During my investigation I will use stratified random sampling because it is more likely to give a sample which is representative of the population. I will use a stratified random sample of size 30 in each case.

The data I will use is quantitive and continuous data. The heights of pupils are given in centimetres (Cm), correct to the nearest centimetre.

In order to discover whether my hypothesis is true or false I aim to:-

- Obtain stratified random samples of size 30 for years 7, 9 and 11.
- Find the mean height of both males and females within years 7, 9 and 11.
- Find the standard deviation (a measure of spread/dispersion.) of both males and females within years 7, 9 and 11.

I will present my results using tables and graphs as appropriate.

Year 7

I will start my investigation by looking at pupils in year 7.

Middle

94 Pick Boy

78 Ignore

03 Pick Girl

49Ignore

13 Pick Girl

05 Pick Girl

01 Pick Girl

94 Ignore

38 Pick Girl

08 Pick Girl

72 Pick Boy

07 Pick Girl

76 Pick Boy

15 Pick Girl

04 Ignore

59Ignore

77 Pick Boy

33 Ignore

87 Pick Boy

10 Ignore

53 Ignore

81 Pick Boy

47 Ignore

80 Pick Boy

14 Ignore

My sample of girls are: 59 38 21 24 28 46 47 49 11 54 32 03 13 05 01 38 08 07 15

My sample of boys are: 80 81 87 77 76 72 83 78 86 97 94

Year 9 Female | Height (Cm) | Year 9 Male | Height (Cm) |

59 | 161 | 83 | 175 |

38 | 166 | 78 | 185 |

21 | 154 | 86 | 169 |

24 | 160 | 97 | 181 |

28 | 160 | 94 | 174 |

46 | 155 | 72 | 174 |

47 | 157 | 76 | 179 |

49 | 162 | 77 | 181 |

11 | 170 | 87 | 184 |

54 | 170 | 81 | 185 |

32 | 158 | 82 | 195 |

03 | 171 | ||

13 | 168 | ||

05 | 157 | ||

01 | 165 | ||

45 | 160 | ||

08 | 158 | ||

07 | 163 | ||

15 | 158 |

I will use the data shown above to calculate the mean height and standard deviation for both boys and girls in year 9.

Year 9 Girls

First I am going to find the mean height of a girl in year 9.

x | 154 | 155 | 156 | 157 | 158 | 159 | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 |

f | 1 | 1 | 0 | 2 | 3 | 0 | 3 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 2 | 1 |

Mean = (154×1) (155×1) (156×0) (157×2) (158×3) (159×0) (160×3) (161×1) (162×1) (163×1) (164×0) (165×1) (166×1) (167×0) (168×1) (169×0) (170×2) (171×1)

_____________________________________________________________________19

=154+155+157+157+158+158+158+160+160+160+161+162+163+165+166+168+170+170+171

_____________________________________________________________________19

= 3073÷19

= 161.74 Cm (2 d.p.)

The mean height for girls in year 9 is 161.74 Cm

Now I am going to find the standard deviation for the girls in year 9.

x | f | x² | fx² |

154 | 1 | 23716 | 23716 |

155 | 1 | 24025 | 24025 |

156 | 0 | 0 | 0 |

157 | 2 | 24649 | 49298 |

158 | 3 | 24964 | 74892 |

159 | 0 | 0 | 0 |

160 | 3 | 25600 | 76800 |

161 | 1 | 25921 | 25921 |

162 | 1 | 26244 | 26244 |

163 | 1 | 26569 | 26569 |

164 | 0 | 0 | 0 |

165 | 1 | 27225 | 27225 |

166 | 1 | 27556 | 27556 |

167 | 0 | 0 | 0 |

168 | 1 | 28224 | 28224 |

169 | 0 | 0 | 0 |

170 | 2 | 28900 | 57800 |

171 | 1 | 29241 | 29241 |

= √∑fx²÷∑f−(x)²

= √497511÷19−26160

= √24.96

= 5.10 (2 d.p.)

Year 9 Boys

First I am going to find the mean height of a boy in year 9.

x | 169 | 170 | 171 | 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 | 181 |

f | 1 | 0 | 0 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 1 | 0 | 2 |

182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 | 191 | 192 | 193 | 194 | 195 |

0 | 0 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

Mean= (169×1) (170×0) (171×0) (172×0) (173×0) (174×2) (175×1) (176×0) (177×0) (178×0) (179×1) (180×0) (181×2) (182×0) (183×0) (184×1) (185×2) (186×0) (187×0) (188×0) (189×0) (190×0) (191×0) (192×0) (193×0) (194×0) (195×1)

_____________________________________________________________________11

= 169+174+174+175+179+181+181+184+185+185+195÷11

= 1982÷11

= 180.18 (2 d.p.)

The mean height of a boy in year 9 is 180.18 Cm

Now I am going to find the standard deviation for the boys in year 9.

x | f | x² | fx² |

169 | 1 | 28561 | 28561 |

170 | 0 | 0 | 0 |

171 | 0 | 0 | 0 |

172 | 0 | 0 | 0 |

173 | 0 | 0 | 0 |

174 | 2 | 30276 | 60552 |

175 | 1 | 30625 | 30625 |

176 | 0 | 0 | 0 |

182 | 0 | 0 | 0 |

183 | 0 | 0 | 0 |

184 | 1 | 33856 | 33856 |

185 | 2 | 34225 | 68450 |

186 | 0 | 0 | 0 |

187 | 0 | 0 | 0 |

188 | 0 | 0 | 0 |

189 | 0 | 0 | 0 |

190 | 0 | 0 | 0 |

177 | 0 | 0 | 0 |

178 | 0 | 0 | 0 |

179 | 1 | 32041 | 32041 |

180 | 0 | 0 | 0 |

181 | 2 | 32761 | 65522 |

191 | 0 | 0 | 0 |

192 | 0 | 0 | 0 |

193 | 0 | 0 | 0 |

194 | 0 | 0 | 0 |

195 | 1 | 38025 | 38025 |

= √∑fx²÷∑f−(x)²

= √357412÷11−32465

= √27

= 5.21 (2 d.p.)

Year 11

Now I am going to look at pupils in year 11. I will start by finding the stratified random sample of 30 pupils.

№ of Females 50÷100×30=15=15 Females needed

№ of Males 50÷100×30=15=15 males needed

I will label the girls 00→49 and the boys 50→99.

I have used my calculator and have generated the following random numbers:

421 684 739 016 378 709 308 106 448 318 329 572 169 899 698 074 710 339 797 348 600 149 431 918 135 118

I want to obtain two digit random numbers from these random numbers, so I pair the digits together.

42|1 6|84 |73|9 0|16 |37|8 7|09 |30|8 1|06 |44|8 3|18 |32|9 5|72 |16|9 8|99 |69|8 0|74 |71|0 3|39 |79|7 3|48 |60|0 1|49 |43|1 9|18 |13|5 1|18|

42 Pick Girl

16 Pick Girl

84

Conclusion

0

2

0

157.5<x<167.5

|||

3

10

0.3

167.5<x<171.5

|||| |

6

4

1.5

171.5<x<176.5

||||

4

5

0.8

176.5<x<186.5

||

2

10

0.2

186.5<x<191.5

0

5

0

191.5<x<195.5

0

4

0

195.5<x<199.5

0

4

0

The histograms I have drawn further illustrate my results. The histogram for year 7 girls showed that their heights were not very dispersed. However, the histograms for year 7 boys showed a greater dispersion, this is also the same for years 9 and 11.

The boys in year 7 showed the greatest dispersion of heights.

Conclusion and evaluation

My hypothesis stated that “On average boys are taller than girls and boy’s heights are more dispersed than girl’s heights.” My hypothesis is supported by my year 7, 9 and 11 results as can be seen from my summary of results table and my histograms. These results are only valid for the school I have investigated. If I were to look at another sample from another school then my results may be different. If I were to attempt this investigation again, I would:-

- Look at a number of different schools, including primary schools and colleges and I would include all of the year groups.
- Look at school in different parts of the country.
- Take a large sample of the pupils.

In this way, my results would be more representative of the population as a whole, and I would be more likely to eliminate any anomalous results from my investigation. I could further extend this investigation by looking at other measurements such as hand span, head circumference etc to see whether these measurements fall in line with my hypothesis i.e. that on average boys have larger measurements than girls and that their measurements are more dispersed than girls measurements.

Page of

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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