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• Level: GCSE
• Subject: Maths
• Word count: 4731

# Hypothesis&quot;The taller you are, the bigger is your foot length&quot;. 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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