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# The heights of 16-18 year old young adults varies between males and females. My prediction is that the majority of males are taller than females.

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Introduction

Statistics coursework

The heights of 16-18 young adults varies between males and females.  My prediction is that the majority of males are taller than females.

I have decided to take a sample of 100 16-18 young adults from Havering Sixth Form College and measure their heights with a tape measure.  My two populations will be male and females and I will obtain 50 male heights and 50 female heights.  I have chosen to take a sample of 100 because small sample sizes may give inaccurate results whereas a larger sample size may be impractical and time consuming.  Therefore I feel a sample size of 100 will give a efficient set of results and a meaningful conclusion could be deduced.

To insure that the data I collected wasn’t biased I didn’t look at each persons height to ensure that the data I collected was even for both populations and within both populations.  Also because height isn’t affected by whether you are athletic or not or whether you eat lots or who you are friends with, the data I collected cant be bias for that aspect of my data collection and also I didn’t collect my

Middle

5ft 10inc

70

4900

1

70

4900

5ft 11inc

71

5041

1

71

5041

6ft

72

5184

1

72

5184

6ft 1inc

73

5329

1

73

5329

Total

50

3228

208854

Mean

64.56

Variance

9.0864

Heights of 16-18 year old males

x (inches)

x^2

F

xF

x^2F

5ft 2inc

62

3844

1

62

3844

5ft 3inc

63

3969

0

0

0

5ft 4inc

64

4096

2

128

8192

5ft 5inc

65

4225

2

130

8450

5ft 6inc

66

4356

2

132

8712

5ft 7inc

67

4489

3

201

13467

5ft 8inc

68

4624

3

204

13872

5ft 9inc

69

4761

6

414

28566

5ft 10inc

70

4900

4

280

19600

5ft 11inc

71

5041

7

497

35287

6ft

72

5184

10

720

51840

6ft 1inc

73

5329

6

438

31974

6ft 2inc

74

5476

2

148

10952

6ft 3inc

75

5625

1

75

5625

6ft 4inc

76

5776

1

76

5776

Total

50

3505

246157

Mean

70.1

Variance

9.13

Conclusion

If I had time I would have extended my problem by widening the age of males and females as I only managed to obtain the heights if males and females aged 16-18.  I could have increased this by including younger and older populations.

I could have concentrated my data collection on children aged 10-15 to compare the difference in height of all 10 year olds up to the age of 15.  I could have also compared the difference in the heights of boys and girls as the age increases from age 10-15 to see if girls increase in height more gradually than boys do as they might shoot up at a certain age, or maybe it occurs the other way round.

If I decided to keep to the data I had collected I could have adapted it by seeing if that the taller a person is, the bigger their shoe size would be and the shorter a person is, the smaller their shoe size would be.

Formulae and definitions

Variance

Mean

Standard error     s.e. = σ

s.e.                                 √n

Unbiased estimate    ( n-1 ) S² = σ n-1

n

Confidence intervals

C.I.

μ =  ±   x  σ n-1

√ n

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5 star(s)

An excellent piece of work showing good use of Normal distribution, the central limit theorem and confidence intervals. 5 stars

Marked by teacher Mick Macve 18/03/2012

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