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# maths coursework-Height and Weight of Pupils and other Mayfield High School investigations

Extracts from this document...

Introduction

At a Mayfield High School

Introduction

This investigation is based upon the students of Mayfield High School, a fictitious school although the data presented is based on a real school. The total number of students in the school is 1183.

...read more.Middle

43

1849

47

2209

39

1521

49

2401

59

3481

45

2025

43

1849

51

2601

68

4624

38

1444

32

1024

47

2209

60

3600

65

4225

35

1225

53

2809

44

1936

44

1936

75

5625

56

3136

75

5625

72

5184

54

2916

45

2025

1547

83663

µ = 51.56667

Standard deviation = √83663 – 51.56667²

30

Standard deviation = 11.386 (3 d.p)

From this evidence I can see that the mean for boys’ weight is not a realistic way of interpreting the data and the mean is unreliable.

Year Group | Number of Boys | Number of Girls | Total |

7 | 151 | 131 | 282 |

8 | 145 | 125 | 270 |

9 | 118 | 143 | 261 |

10 | 106 | 94 | 200 |

11 | 84 | 86 | 170 |

Boys Height | |

x | x² |

147 | 21609 |

164 | 26896 |

136 | 18496 |

171 | 29241 |

165 | 27225 |

151 | 22801 |

160 | 25600 |

162 | 26244 |

151 | 22801 |

170 | 28900 |

156 | 24336 |

152 | 23104 |

166 | 27556 |

165 | 27225 |

155 | 24025 |

160 | 25600 |

153 | 23409 |

170 | 28900 |

156 | 24336 |

169 | 28561 |

164 | 26896 |

156 | 24336 |

171 | 29241 |

163 | 26569 |

183 | 33489 |

174 | 30276 |

188 | 35344 |

179 | 32041 |

162 | 26244 |

192 | 36864 |

4911 | 808165 |

µ = 163.7 |

Standard deviation = √808165 – 163.7²

30

Standard deviation = 11.88 (2 d.p)

I can see that my mean for boys’ height isn’t a good way to judge my data. It is unreliable as the standard deviation is quite high.

## Girls Weight | |

x | x² |

47 | 2209 |

45 | 2025 |

53 | 2809 |

40 | 1600 |

47 | 2209 |

65 | 4225 |

38 | 1444 |

43 | 1849 |

50 | 2500 |

52 | 2704 |

51 | 2601 |

45 | 2025 |

40 | 1600 |

51 | 2601 |

72 | 5184 |

52 | 2704 |

51 | 2601 |

40 | 1600 |

40 | 1600 |

55 | 3025 |

48 | 2304 |

41 | 1681 |

52 | 2704 |

50 | 2500 |

52 | 2704 |

55 | 3025 |

42 | 1764 |

80 | 6400 |

64 | 4096 |

86 | 7396 |

1547 | 83689 |

µ = 51.56667 |

Standard deviation = √83689 – 51.56667²

30

Standard deviation = 10.963 (3 d.p)

From the outcome of the standard deviation for girls’ weight, I can see that the mean for the girls’ weight isn’t a good way to interpret the data. The mean is unreliable.

Girls Height | |

x | x² |

161 | 25921 |

150 | 22500 |

172 | 29584 |

146 | 21316 |

148 | 21904 |

162 | 26244 |

143 | 20449 |

156 | 24336 |

160 | 25600 |

159 | 25281 |

162 | 26244 |

150 | 22500 |

143 | 20449 |

167 | 27889 |

165 | 27225 |

155 | 24025 |

145 | 21025 |

164 | 26896 |

153 | 23409 |

158 | 24964 |

170 | 28900 |

140 | 19600 |

152 | 23104 |

163 | 26569 |

178 | 31684 |

170 | 28900 |

173 | 29929 |

190 | 36100 |

189 | 35721 |

200 | 40000 |

4844 | 788268 |

µ=161.4667 |

Standard deviation = √788268 - 161.4667²

30

Standard deviation = 14.287 (3 d.p)

The standard deviation for girls’ height is high and therefore I can not use the mean to judge my data. The mean is unreliable.

- From the results I have got for standard deviation I can see that the mean for girls and boy’s weights and heights isn’t a reliable way to interpret the data I have collected.

Product-moment correlation coefficient r (PMCC)

The product moment correlation coefficient is good for seeing how strong the correlations are on my scatter graphs. I can predict that the correlation for girls will be stronger than that for boys.

Formula: r = Sxy

√ (SxxSyy)

Sxy = ∑xy - ∑x∑y

n

Sxx = ∑x² - (∑x) ²

n

Syy = ∑y² - (∑y) ²

n

PMCC for boys | ||||

x | y | x² | y² | xy |

1.47 | 41 | 2.1609 | 1681 | 60.27 |

1.64 | 50 | 2.6896 | 2500 | 82 |

1.36 | 45 | 1.8496 | 2025 | 61.2 |

1.71 | 49 | 2.9241 | 2401 | 83.79 |

1.65 | 64 | 2.7225 | 4096 | 105.6 |

1.51 | 59 | 2.2801 | 3481 | 89.09 |

1.60 | 43 | 2.56 | 1849 | 68.8 |

1.62 | 47 | 2.6244 | 2209 | 76.14 |

1.51 | 39 | 2.2801 | 1521 | 58.89 |

1.70 | 49 | 2.89 | 2401 | 83.3 |

1.56 | 59 | 2.4336 | 3481 | 92.04 |

1.52 | 45 | 2.3104 | 2025 | 68.4 |

1.66 | 43 | 2.7556 | 1849 | 71.38 |

1.65 | 51 | 2.7225 | 2601 | 84.15 |

1.55 | 68 | 2.4025 | 4624 | 105.4 |

1.60 | 38 | 2.56 | 1444 | 60.8 |

1.53 | 32 | 2.3409 | 1024 | 48.96 |

1.70 | 47 | 2.89 | 2209 | 79.9 |

1.56 | 60 | 2.4336 | 3600 | 93.6 |

1.69 | 65 | 2.8561 | 4225 | 109.85 |

1.64 | 35 | 2.6896 | 1225 | 57.4 |

1.56 | 53 | 2.4336 | 2809 | 82.68 |

1.71 | 44 | 2.9241 | 1936 | 75.24 |

1.63 | 44 | 2.6569 | 1936 | 71.72 |

1.83 | 75 | 3.3489 | 5625 | 137.25 |

1.74 | 56 | 3.0276 | 3136 | 97.44 |

1.88 | 75 | 3.5344 | 5625 | 141 |

1.79 | 72 | 3.2041 | 5184 | 128.88 |

1.62 | 54 | 2.6244 | 2916 | 87.48 |

1.92 | 45 | 3.6864 | 2025 | 86.4 |

49.11 | 1547 | 80.8165 | 83663 | 2549.05 |

r= (2549.05) - (49.11X1547)

30 .

√ (80.8165) – (49.11)² X (83663) – (1547) ²

- 30

r = 16.611

40.58170188

r = 0.409332

- I can see from calculating the PMCC, that my strength for the correlation between the two variables, height and weight, for boys is weak.

PMCC for girls | ||||

x | y | x² | y² | xy |

1.61 | 47 | 2.5921 | 2209 | 75.67 |

1.50 | 45 | 2.25 | 2025 | 67.5 |

1.72 | 53 | 2.9584 | 2809 | 91.16 |

1.46 | 40 | 2.1316 | 1600 | 58.4 |

1.48 | 47 | 2.1904 | 2209 | 69.56 |

1.62 | 65 | 2.6244 | 4225 | 105.3 |

1.43 | 38 | 2.0449 | 1444 | 54.34 |

1.56 | 43 | 2.4336 | 1849 | 67.08 |

1.60 | 50 | 2.56 | 2500 | 80 |

1.59 | 52 | 2.5281 | 2704 | 82.68 |

1.62 | 51 | 2.6244 | 2601 | 82.62 |

1.50 | 45 | 2.25 | 2025 | 67.5 |

1.43 | 40 | 2.0449 | 1600 | 57.2 |

1.67 | 51 | 2.7889 | 2601 | 85.17 |

1.65 | 72 | 2.7225 | 5184 | 118.8 |

1.55 | 52 | 2.4025 | 2704 | 80.6 |

1.45 | 51 | 2.1025 | 2601 | 73.95 |

1.64 | 40 | 2.6896 | 1600 | 65.6 |

1.53 | 40 | 2.3409 | 1600 | 61.2 |

1.58 | 55 | 2.4964 | 3025 | 86.9 |

1.7 | 48 | 2.89 | 2304 | 81.6 |

1.4 | 41 | 1.96 | 1681 | 57.4 |

1.52 | 52 | 2.3104 | 2704 | 79.04 |

1.63 | 50 | 2.6569 | 2500 | 81.5 |

1.78 | 52 | 3.1684 | 2704 | 92.56 |

1.70 | 55 | 2.89 | 3025 | 93.5 |

1.73 | 42 | 2.9929 | 1764 | 72.66 |

1.90 | 80 | 3.61 | 6400 | 152 |

1.89 | 64 | 3.5721 | 4096 | 120.96 |

2.00 | 86 | 4 | 7396 | 172 |

48.44 | 1547 | 78.8268 | 83689 | 2534.45 |

r= (2534.45) - (48.44X1547)

30 .

√ (78.8268) – (48.44)² X (83689) – (1547) ²

30 30

r = 36.56066667

48.96490299

r = 0.74667

- I can see from the answer that my prediction was right. The correlation for girls’ height and weight is definitely stronger than that for boys. This tells me that there is a better relationship between height and weight for girls more than boys.

Conclusion from random sampling

- There is a positive correlation between height and weight. In general tall people will weigh more than smaller people.

- The points on the scatter diagram for the girls are less dispersed about the line of best fit than those for boys. This suggests that the correlation is better for girls than for boys.

- The points on the scatter diagrams for boys and girls are less dispersed than the points on the scatter diagram for mixed sample of boys and girls. This suggests that the correlation between height and weight is better when girls and boys are considered separately.

- I can use the scatter diagrams to give reasonable estimates of height and weight. This can be done either by reading from the graph or using the equations for the line of best fit.

- The cumulative frequency curves confirm that boys and girls have quite a close height and weight, with girls being slightly higher in weight and boys slightly higher in height.

- The median for boys is higher in height and the median for girls is higher in weight.

- From the box and whisker diagrams I can conclude that, in general boys are taller than girls, but not exclusively so. The cumulative frequency curves can be used to estimate that 23% of girls have a higher height than 172 cm, the upper quartile height of boys.

- Also from the box and whisker diagrams I can conclude that in general girls weigh more than boys but not exclusively so. The cumulative frequency curves can be used to estimate that 23% of boys have a higher weight than girls above 60 kg. This could also be a result of my sampling which has more students from year 7 and 8 then 9, 10 or 11. This could mean more lighter people than heavier people

- I could have had a greater confidence in these results if we had taken larger samples. Also, my predictions are based on general trends observed in the data. In both samples there were exceptional individuals whose results fell outside the general trend.

- When age is taken to consideration, the correlation between height and weight will be better than when age is not considered.

This was based upon 60 students sampled at random. To ensure that the students from different age groups are represented equally I will now take a stratified sample.

Stratified Sample

Year Group | Number of Boys | Number of Girls | ...read more.
Conclusion
- The standard deviation showed me that the mean isn’t a reliable way of interpreting my data.
- The product-moment correlation coefficient shows that the correlation between height and weight is stronger for girls than for boys.
Final conclusion - In general the taller a person is, the more they will weigh.
- There is a positive correlation between height and weight. In general tall people will weigh more than smaller people.
- The points on the scatter diagram for the girls are less dispersed about the line of best fit than those for boys. This suggests that the correlation is better for girls than for boys. Also, the points on the scatter diagrams for boys and girls are less dispersed than the points on the scatter diagram for mixed sample of boys and girls. This suggests that the correlation between height and weight is better when girls and boys are considered separately.
- There therefore is a positive correlation between height and weight across the school as a whole. This correlation seems to be stronger when separate genders are considered
- I can use the scatter diagrams to give reasonable estimates of height and weight. This can be done either by reading from the graph or using the equations for the line of best fit.
- There is a better relationship between height and weight when people in the school are taken into proportion in each year.
- I could have had a greater confidence in these results if we had taken larger samples. Also, my predictions are based on general trends observed in the data. In both samples there were exceptional individuals whose results fell outside the general trend.
This coursework was both interesting and enjoyable to do although it was hard work. I have learnt a few things from this coursework such as standard deviation and product-moment correlation coefficient, both of which I had previously not known about. 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. ## Found what you're looking for?- Start learning 29% faster today
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