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  • Level: GCSE
  • Subject: Maths
  • Word count: 4294

Data Analysis Investigation-Higher Tier

Extracts from this document...

Introduction

image00.jpg

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.

...read more.

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

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

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

...read more.

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.

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