# data handling

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Introduction

Jason Choi 10B Maths Set 0 Maths Coursework

## Introduction

## I have chosen three categories, which are the height, hand span and the shoe size from the data. My first hypothesis is that taller people will have

## bigger feet. My second hypothesis is that taller people will have bigger hand spans. I think that there will be a positive correlation between the height with shoe and hand size because it’s common sense. Most people I see on the streets have big hands and feet when they are tall. I think that both correlations will be very high because of this.

## I picked a sample of 50 people because 50 out of about 261 pupils will be just about 20% of the people. It uses some of the people and 50 is a nice number to work with. I picked the sample of 50 by using stratified sampling since a random choice is not representative. The sample might contain all 50 boys or all 50 girls might it is random. Also, a stratified sample is more representative because it would be accurate by being based on the information, but it is not perfect.

The data that I needed to stratify are the date of births and the gender of the pupils because older pupils are normally taller.

Months | Boys | Girls | Total Amount |

September | 11 | 9 | 20 |

October | 14 | 6 | 20 |

November | 7 | 13 | 20 |

December | 9 | 17 | 26 |

January | 13 | 6 | 19 |

February | 17 | 10 | 27 |

March | 15 | 17 | 32 |

April | 9 | 8 | 17 |

May | 9 | 11 | 20 |

June | 12 | 13 | 25 |

July | 9 | 16 | 25 |

August | 4 | 6 | 10 |

129 | 132 | 261 |

Middle

39.5

5

41.5

2

4

158

42

5

41.5

-0.5

0.25

157

43

5

41.5

-1.5

2.25

155

44.5

7

27.5

-17

289

155

44.5

5

41.5

-3

9

154

46.5

4.5

47

0.5

0.25

154

46.5

4

48.5

2

4

153

48

5

41.5

-6.5

42.25

150

49

5

41.5

-7.5

56.25

145

50

3.5

50

0

0

3356.5

The answer was 3356.5 when I added them all up. I substituted the answer into the formula.

The answer 0.84 is very close to 1 so it has a very strong correlation. This suggests that taller people have bigger feet.

Hypothesis 2, taller people have bigger hand spans.

I rank the height of the pupils in order from 1-50. I did the same again for the hand-span, ranking them from 1-50. I calculated their differences in ranks and squared the difference for all of them.

Height nearest cm | Ranking Order | Hand Span, nearest mm | Ranking Order | (d)difference | d*d |

193 | 1 | 240 | 3 | 2 | 4 |

191 | 2 | 250 | 1 | -1 | 1 |

188 | 3 | 241 | 2 | -1 | 1 |

185 | 4.5 | 190 | 29.5 | 25 | 625 |

185 | 4.5 | 220 | 10 | 5.5 | 30.25 |

182 | 6 | 210 | 15.5 | 9.5 | 90.25 |

181 | 7 | 235 | 4.5 | -2.5 | 6.25 |

180 | 8 | 235 | 4.5 | -3.5 | 12.25 |

178 | 9 | 210 | 15.5 | 6.5 | 42.25 |

177 | 10 | 210 | 15.5 | 5.5 | 30.25 |

176 | 11 | 230 | 7 | -4 | 16 |

175 | 12 | 220 | 10 | -2 | 4 |

174 | 13.5 | 230 | 7 | -6.5 | 42.25 |

174 | 13.5 | 200 | 22 | 8.5 | 72.25 |

173 | 16 | 190 | 29.5 | 13.5 | 182.25 |

173 | 16 | 200 | 22 | 6 | 36 |

173 | 16 | 210 | 15.5 | -0.5 | 0.25 |

172 | 18 | 212 | 13 | -5 | 25 |

171 | 19 | 220 | 10 | -9 | 81 |

170 | 21.5 | 215 | 12 | -9.5 | 90.25 |

170 | 21.5 | 170 | 44.5 | 23 | 529 |

170 | 21.5 | 200 | 22 | 0.5 | 0.25 |

170 | 21.5 | 170 | 44.5 | 23 | 529 |

169 | 24.5 | 195 | 26 | 1.5 | 2.25 |

169 | 24.5 | 180 | 37.5 | 13 | 169 |

168 | 27 | 230 | 7 | -20 | 400 |

168 | 27 | 180 | 37.5 | 10.5 | 110.25 |

168 | 27 | 150 | 50 | 23 | 529 |

167 | 29.5 | 180 | 37.5 | 8 | 64 |

167 | 29.5 | 200 | 22 | -7.5 | 56.25 |

165 | 31.5 | 161 | 48 | 16.5 | 272.25 |

165 | 31.5 | 200 | 22 | -9.5 | 90.25 |

164 | 33.5 | 180 | 37.5 | 4 | 16 |

164 | 33.5 | 190 | 29.5 | -4 | 16 |

163 | 35 | 198 | 25 | -10 | 100 |

163 | 35 | 201 | 19 | -16 | 256 |

163 | 35 | 207 | 18 | -17 | 289 |

160 | 39.5 | 185 | 32.5 | -7 | 49 |

160 | 39.5 | 181 | 34 | -5.5 | 30.25 |

160 | 39.5 | 180 | 37.5 | -2 | 4 |

160 | 39.5 | 180 | 37.5 | -2 | 4 |

158 | 42 | 191 | 27 | -15 | 225 |

157 | 43 | 170 | 44.5 | 1.5 | 2.25 |

155 | 44.5 | 185 | 32.5 | -12 | 144 |

155 | 44.5 | 176 | 41 | -3.5 | 12.25 |

154 | 46.5 | 170 | 44.5 | -2 | 4 |

154 | 46.5 | 160 | 49 | 2.5 | 6.25 |

153 | 48 | 190 | 29.5 | -18.5 | 342.25 |

150 | 49 | 170 | 44.5 | -4.5 | 20.25 |

145 | 50 | 170 | 44.5 | -5.5 | 30.25 |

5694 |

The answer was 5694 when I added them all up. I substituted the answer into the formula.

The answer 0.73 is close to 1 so it has a strong correlation. This suggests that taller people have bigger hand spans but this correlation is not as strong as the other correlation. For hypothesis 1, the answer was 0.16 from perfect positive correlation. For hypothesis 2, the answer was 0.27 from perfect positive correlation.

So Hypothesis 1 has a stronger correlation. A taller person is more likely to have bigger feet than a large hand span.

Just for the Height

Conclusion

150

24

5

16.5

-7.5

56.25

F

145

25

3.5

25

0

0

967

The answer was 967 when I added them all up. I substituted the answer into the formula.

The answer 0.63 is not too close to 1 so it has a moderate correlation. This suggests that taller boys are more likely than girls to have bigger feet.

Conclusion

In the end, I think that Spearman’s Rank was the best because it gave a very accurate answer. It was difficult to work out all the answers but in the end, tall people have bigger feet and hand spans. But the data were only from year 10s in Salendine Nook High School so it only really proves that tall people in year 10 attending Salendine Nook High School have bigger feet and hand spans. However it could mean that all pupils in year 10 in different schools have bigger feet and hand spans. We don’t and we won’t know though as there are many other factors such as cultural background that we need to know to prove our results right. The data is also flawed as lots of information was missing and pupils imputed their data in differently.

I think that I chose the right groups to prove my hypothesis. To improve this and make my results better, I could get other schools’ data or maybe different years in my school. People like shoe or glove makers can use this data and design more shoes in region of the average size. In the end, I think I proved that my hypothesis is correct.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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## Here's what a teacher thought of this essay

A good thorough piece of work but many of the formulae and diagrams are not showing properly or have simply been omitted. However, reasonable use of Speasrman?s and standard deviation. 3 stars

Marked by teacher Mick Macve 18/03/2012