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Height and foot sizes

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Introduction

Samantha Bennett

Maths Coursework

Statistics

My task is to produce a statistical report with the data I have been given. Which is on an excel spread sheet, the data consists of Name, Year group, Gender, Maths set, Registration group, Height and foot length of every person who was present on the day the statistics were taken, to ensure some kind of confidentially there is only the first letter of the forename and the first three letters of the surname in the data. All the measurements were taken to the nearest centimetre. Some of the data is missing such as the set or gender because the information was unavailable but this makes the statistics realistic because in modern day life information would be missing or unavailable. The data collected is primary data because I was present and participated when it was being collected. The data was collected by measuring the height of every person to the nearest centimetre and their right foot to the nearest centimetre. 6th

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Middle

5

0.6

163-172

5

10

0.5

Standard width 1

My histograms give a good visual impression of my data.

The simplest measure of spread is the range but it does not take in to account the extremes in the data, A better measure of spread is the inter quartile range because it ignores the extreme values I will get the inner quartile range from a cumulative frequency graph. I will draw a cumulative frequency graph for each years 8 and 11 putting the girls and boys on the same graph    

Year 8 girls-

Height

frequency

cumulative frequency

140-145

4

4

146-150

4

8

151-155

7

15

156-160

6

21

161-165

4

25

166-170

3

28

171-175

2

30

Year 8 boys-

Height

frequency

cumulative frequency

140-145

6

6

146-150

4

10

151-155

12

22

156-160

6

28

161-165

10

38

166-170

2

40

Year 11 girls-

Height

frequency

cumulative frequency

156-160

11

11

161-165

13

24

166-170

6

30

171-175

1

31

Year 11 boys-

Height

frequency

cumulative frequency

161-165

1

1

166-170

5

6

171-175

9

15

176-180

13

28

181-185

10

38

186-190

0

38

191-195

1

39

As you can see on my cumulative frequency graphs I have marked the inner quartile ranges in. in Year 8 a better measure of spread would be the inner quartile range this is –

Girls: 167.5-150=17.5

Boys: 162.5-150=12.5

And year 11

Girls: 166-155.5= 10.5

Boys: 181-173.5= 7.5

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Conclusion

All I can do is plot a scatter diagram as I do not have enough statistics to do this question in detail.

As you can see my scatter diagram has a positive correlation so year 10 boys in our school follow the statement do tall people have big feet. Of course I only used a small sample and all from the Anglo European school, so my report is not reliable as there may be something peculiar about the people in my school.

From my report I can see that at the beginning of the school girls are slightly taller but by the end of the school boys are a lot taller then the girls. If I could have continued my report I would have liked to do the standard deviation of al the years and would have liked the produce a cumulative frequency graph for more then 2 years. I would have also liked to attempt the harder question- tall people have big feet on more then year 9 boys.  

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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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