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Body Statistics Maths Investigation

Extracts from this document...

Introduction

Adam Wright

Maths Statistics Coursework

Body Statistics

As we grow up we change - or do we? Boys are different from girls - or are they?

Use samples from different age groups for both sexes. Choose two measurable statistics that can be sampled easily and sensitively. You need one statistic you think will be different and one you do not think will be different and use a sample for each.

Make a hypothesis.

Collecting the data

 We collected data from those who were both older and younger than us. I was directly involved in data capture of body statistics for two classes of year sevens who had maths simultaneously as us. We chose to survey the whole of the accessible population because of the relatively small size of it. We chose to sample to classes because the amount of data we would collect, about 60 sets, would be about correct. It is large enough to collect in a reasonable amount of time. It is also large enough to be able to discount any obvious discrepancies without the data figure falling below 50.

We presented the children with a form which they complete themselves with basic information such as shoe sizes.

...read more.

Middle

64

20

163

27.5

24

3.5

12.25

20

160

23.5

24

-0.5

0.25

20

158

22

24

-2

4

20

154

15.5

24

-8.5

72.25

20

154

15.5

24

-8.5

72.25

19

161

25.5

20

5.5

30.25

19

155

17

20

-3

9

19

151

13.5

20

-6.5

42.25

18.5

156

18

18

0

0

18.3

149

10.5

17

-6.5

42.25

18

157

19

14.5

4.5

20.25

18

151

13.5

14.5

-1

1

18

150

12

14.5

-2.5

6.25

18

145

5.5

14.5

-9

81

17.6

157

19

12

7

49

17

145

5.5

10.5

-5

25

17

144

3

10.5

-7.5

56.25

16.5

144

3

9

-6

36

16

167

29

6.5

22.5

506.25

16

163

27.5

6.5

21

441

16

149

10.5

6.5

4

16

16

144

3

6.5

-3.5

12.25

15.9

143

1

4

-3

9

15

147

8

3

5

25

14

147

8

1.5

6.5

42.25

14

147

8

1.5

6.5

42.25

Total  

1761

I will use the following formulae to find out if there is any correlation between the two sets of ranking.

P = 1-   6∑d²

N(n²-1)

Where N is the number of pairs of data.

The result of the calculations is 0.61 that is an encouraging result when the population size is taken into account. This figure is well above the minimum point at which rank coefficient is likely. This is a good result to prove the theory above. The minimum figure below 1 of which rank coefficient is probable is 0.46. Therefore in this case there is a clear link between the rankings of the two sets of data. This proves the hypotheses B by proving strongly that there is a clear link between hand span and height. Therefore we can say quite confidently that the all bodies are roughly within set proportions.

Hypothesis C        Heart rate and age are unrelated.

To find out if this hypothesis is true or untrue I will work out the mean for each year.

...read more.

Conclusion

In response to the to my original hypotheses the age and pulses are related the results would suggest so. But I think we need to take into account the spread of the ages we are looking at. Although between all three there is an increase of sorts the difference between the first two age groups is large the difference in the results is relatively minor. The age gap between the year 11 and 12 data is just a single year and we see a vast increase. When we see this on a graph with the means plotted the absurdity of the results is all to apparent. Therefore in future if repeating this I would have to use a bigger population as to find better results. As the population size increases it will better represent the full population. Therefore I would safely dismiss any relationship between age and pulse rate over the age we have covered.

Adam Wright                                                                                             Statistics C/W

...read more.

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