# Hypothesis"The taller you are, the bigger is your foot length". I think my hypothesis is true because there is a positive correlation between the heights and foot length.

Extracts from this document...

Introduction

Designing and Planning

Introduction

I am investigating a hypothesis using the data from the Census at School Data Selector, to see whether it is proved correct.

Hypothesis

“The taller you are, the bigger is your foot length”.

I think my hypothesis is true because there is a positive correlation between the heights and foot length.

Plan of action-collecting data

I will collect the data I need from the Census at School Data Selector. The data will be useful because it will give me an opportunity to do a preliminary example test on the hypothesis which I am trying to prove. And I will do histograms to see if my data was reliable. Then I will use the data from a statsfile which is a selection of results ranged from ages 7 to 17 collected in 2002-2003, it is a secondary data. I will collect 50 samples of random sampling and a fairer 100 samples of stratified sampling to test the hypothesis. I will try to make sure that my results are reliable by using the stratified sample I’m going to take from the statsfile. To test its reliability, I will do a histogram. I will have quantitative data because all my samples are numerical. My quantitative data will be continuous. I will record the data I collected in Microsoft Excel.

Plan of action- Processing and representing data

Middle

F

14

172

25

674

F

14

154

23

591

F

14

180

25

646

F

14

171

24

698

F

14

154

23

572

F

14

166

24

742

M

14

210

35

685

F

14

161

23

639

F

14

165

22

726

F

14

172

26

746

M

14

170

25

658

F

14

160

24.5

909

M

14

156

23

857

M

14

182

27

708

F

14

162

25

488

F

14

165

19

893

M

14

176

30

716

F

14

166

24

871

M

14

176

30

653

F

14

155

22

650

F

14

173

27

509

F

14

200

24

913

M

14

178

30

701

F

14

169

22

986

M

15

180

27

973

M

15

176

23

985

M

15

191

28

990

M

15

181

29

949

F

15

171

23

973

M

15

176

23

936

F

15

160

21

958

F

15

154

19

991

M

15

175

24

987

M

15

110

27

1033

F

16

166

21.5

1065

M

16

190

35

1048

F

16

166

23

1035

F

16

168

26

Cumulative frequency

Height | Number of people | Cumulative frequency |

110≤h<120 | 1 | 1 |

120≤h<130 | 2 | 3 |

130≤h<140 | 0 | 3 |

140≤h<150 | 4 | 7 |

150≤h<160 | 29 | 36 |

160≤h<170 | 31 | 67 |

170≤h<180 | 25 | 92 |

180≤h<190 | 4 | 96 |

190≤h<200 | 2 | 98 |

200≤h<210 | 1 | 99 |

210≤h<220 | 1 | 100 |

It shows the measure of spread on the middle 50% of the data (between the upper and the lower quartile)

The stratified sample has no skew, mode=median=mean, as the median- lower quartile= higher quartile- median:

160- 153= 167- 160

7=7

From the graph, we can see that my data is reliable as the interquartile range is 14 cm which is relatively small. This shows that most of my data is gathered around the mean which follows the normal pattern we expects.

Standard deviation

It is mainly used to compare to sets of data. It’s another measure of spread or dispersion about the mean in a more accurate way than the range or interquartile range. It gives a more detailed picture of the way in which the data is dispersed about the mean as the centre of the distribution.

Standard deviation (s.d) =

Where ∑ represents the sum

x represents an item of data

n represents the number of item of data

The symbol is the mean where

Variance = the mean of the squares minus the square of the mean

Height (cm) mid interval frequency

x | f | fx | x2 | fx2 | |

110≤h<120 | 115 | 1 | 115 | 13225 | 13225 |

120≤h<130 | 125 | 2 | 250 | 15625 | 31250 |

130≤h<140 | 135 | 0 | 0 | 18225 | 0 |

140≤h<150 | 145 | 4 | 580 | 21025 | 84100 |

150≤h<160 | 155 | 29 | 4495 | 24025 | 696725 |

160≤h<170 | 165 | 31 | 5115 | 27225 | 843975 |

170≤h<180 | 175 | 25 | 4375 | 30625 | 765625 |

180≤h<190 | 185 | 4 | 740 | 34225 | 136900 |

190≤h<200 | 195 | 2 | 390 | 38025 | 76050 |

200≤h<210 | 205 | 1 | 205 | 42025 | 42025 |

210≤h<220 | 215 | 1 | 215 | 46225 | 46225 |

∑ | 100 | 16480 | 2736100 |

Mean, =16480 / 100=164.8

Variance, = 2736100 / 100 – 164.82= 201.96

Standard deviation, s = √201.96= 14.21 (2 d.p), so s.d. of the height is 8.6%

Any values that don’t lie within 2 s.d. away from the mean are outliers:

164.8± 14.21*2

So values <136.38cm or >193.22cm are outliers.

Foot length (cm) mid interval frequency

x | f | fx | x2 | fx2 | |

15≤f<20 | 17.5 | 5 | 87.5 | 306.25 | 1531.25 |

20≤f<25 | 22.5 | 55 | 1237.5 | 506.25 | 27843.75 |

25≤f<30 | 27.5 | 33 | 907.5 | 756.25 | 24956.25 |

30≤f<35 | 32.5 | 5 | 162.5 | 1056.25 | 5281.25 |

35≤f<40 | 37.5 | 2 | 75 | 1406.25 | 2812.5 |

∑ | 100 | 2470 | 62425 |

Conclusion

-8.29

-3.253

-0.71262

-4.83756

8.71

0.747

0.74872

1.11087

-9.29

-1.253

-0.79858

-1.86335

16.71

0.747

1.43642

1.11087

7.71

-0.253

0.66276

-0.37624

-9.29

-1.253

-0.79858

-1.86335

2.71

-0.253

0.23296

-0.37624

46.71

10.747

4.01526

15.98196

-2.29

-1.253

-0.19685

-1.86335

1.71

-2.253

0.14699

-3.35046

8.71

1.747

0.74872

2.59798

6.71

0.747

0.5768

1.11087

-3.29

0.247

-0.28281

0.36732

-7.29

-1.253

-0.62666

-1.86335

18.71

2.747

1.60834

4.08509

-1.29

0.747

-0.11089

1.11087

1.71

-5.253

0.14699

-7.81178

12.71

5.747

1.09257

8.54641

2.71

-0.253

0.23296

-0.37624

12.71

5.747

1.09257

8.54641

-8.29

-2.253

-0.71262

-3.35046

9.71

2.747

0.83469

4.08509

36.71

-0.253

3.15565

-0.37624

14.71

5.747

1.26449

8.54641

5.71

-2.253

0.49084

-3.35046

16.71

2.747

1.43642

4.08509

12.71

-1.253

1.09257

-1.86335

27.71

3.747

2.38199

5.5722

17.71

4.747

1.52238

7.0593

7.71

-1.253

0.66276

-1.86335

12.71

-1.253

1.09257

-1.86335

-3.29

-3.253

-0.28281

-4.83756

-9.29

-5.253

-0.79858

-7.81178

11.71

-0.253

1.00661

-0.37624

-53.29

2.747

-4.58089

4.08509

2.71

-2.753

0.23296

-4.09401

26.71

10.747

2.29603

15.98196

2.71

-1.253

0.23296

-1.86335

4.71

1.747

0.40488

2.59798

Conclusion

My original hypothesis was “the taller you are, the bigger is your foot length” and it’s supported by the overall evidence.

From my preliminary work we established that there is a positive correlation between the height and foot length. This enabled me to carry the investigation further, using the data from stratified sampling which are both random and fair.

I found out the interquartile range and standard deviation to prove the reliability of my results. The correlation coefficient of my sample is 0.38, showing some positive correlation. I also went further and did regression lines where we can estimate values of variable given values of the other if we know one of them.

All this areas I have covered proves my hypothesis to be correct. And this investigation could be developed further. I could investigate the difference in the relationship between height and foot length in different ages, such as 13, 14, 15, 16, 17and 18 years old, where I would expect the relationship to be stronger with older ages as the body proportions varies more with younger children.

Census at School data

Height (cm) | Foot length (cm) |

119 | 20 |

129 | 26 |

130 | 24 |

140 | 21 |

140 | 22 |

140 | 22 |

140 | 24 |

142 | 21 |

142 | 24 |

143 | 21.5 |

144 | 22 |

145 | 22 |

145 | 23.5 |

146 | 21 |

146 | 25.5 |

148 | 21 |

149 | 21 |

149 | 23 |

149 | 24 |

149 | 25 |

149 | 27 |

150 | 20 |

150 | 22 |

151 | 20 |

151 | 24 |

153 | 20 |

153 | 21 |

153 | 22 |

153 | 24 |

154 | 22 |

154 | 22.5 |

154 | 24 |

154 | 26 |

155 | 17 |

155 | 21 |

155 | 23 |

155 | 23 |

155 | 27 |

156 | 20 |

156 | 24 |

156 | 25 |

157 | 20.5 |

157 | 23.5 |

157 | 24.5 |

158 | 22 |

158 | 22 |

158 | 23 |

158 | 24 |

158 | 24 |

159 | 26 |

159 | 27 |

160 | 16 |

160 | 24 |

161 | 23 |

161 | 23.5 |

161 | 24 |

161 | 26 |

162 | 22 |

162 | 22 |

162 | 25 |

162 | 25 |

162 | 27 |

163 | 20 |

163 | 24 |

163 | 24.2 |

163 | 25.5 |

163 | 26.5 |

164 | 19 |

164 | 20 |

164 | 22 |

164 | 24 |

164 | 25 |

165 | 24 |

165 | 25 |

166 | 24 |

166 | 24 |

167 | 23 |

167 | 26 |

168 | 20 |

168 | 24 |

168 | 24.9 |

169 | 26 |

169 | 28 |

170 | 24 |

170 | 24 |

170 | 24 |

170 | 26 |

172 | 30 |

174 | 24 |

174 | 28 |

174 | 32 |

175 | 23 |

175 | 24 |

176 | 26 |

176 | 26 |

177 | 22 |

184 | 27 |

185 | 33.7 |

186 | 29 |

194 | 28 |

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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