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

Data Analysis Investigation-Higher Tier

Extracts from this document...

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.

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