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• Level: GCSE
• Subject: Maths
• Word count: 1181

# Investigating the relationship between the height and arm span of year 10 pupils and the spread of height of boys compared with girls.

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Introduction

Intro:  I will be investigating the relationship between the height and arm span of year 10 pupils and the spread of height of boys compared with girls.

Hypothesis: I believe that there will be a relationship between a persons height and arm span and as one grows in height arm span increases. Also I predict that there will be a greater variation in height in the boys compared with girls.

• For relationship arm span V height I will draw a scatter diagram for my sample of 60 and compare it with the scatter graph for the population. I will calculate the mean arm span and height for my sample and compare it with the mean of the population. By doing this I shall see weather or not my sample is a good representation of the population.
• For heights or arm span of boys and girls separately I will group the data in a frequency table, which will enable me to see the modal class clearly. I will use this frequency table to draw a cumulative frequency curve from which I will find the median and the interquatile range. I will also draw a histogram to observe spread and calculate standard deviation for the boys and girls separately

Middle

158

157

157

168

168161

163

168

143

149

159

160

159

166

175

158

170

165

168

167

163

164

176

165

164

165

167

Grouped frequency tables.

Unfortunately, these samples are still too large to let me look at the data clearly, so I will put them into grouped frequency tables before carrying out my calculations.

Boys

Height (cm)

## Frequency (f)

Cumulative Frequency

Mid point (x)

## Fx

Fx

150<h<155

2

2

152.5

305

4152.5

155<h<160

1

3

157.5

157.5

157.5

160<h<165

4

7

162.5

650

2600

165<h<170

8

15

167.5

1340

10720

170<h<175

7

22

172.5

1207.5

8452.5

175<h<180

6

28

177.5

1065

6390

180<h<185

4

32

182.5

730

2920

185<h<190

1

33

187.5

187.5

187.5

total f = 33                                               fx= 5642.5 fx=35580

Girls

Conclusion

From the histograms, I can see that the boys are fare more spread out than those of the girls, as there are more bars across the range. The modal group for the boys is 165<h<170 and for the girls was 160<h<165 and 165<h<170 because the girls have to modal groups we call this bi-modal.

Conclusion

Having completed the investigation I can now conclude that there is positive correlation between height and arm span between Yr.10 pupils. The mean arm span and Height were similar. There was also a greater dispersion in the height of the boys than the girls.

## Evaluation

Possible errors – how to avoid in future.

• Human error – scale read incorrectly – could avoid this by having second person to double check results.
• Height – Ensure all shoes are taken off.
• Errors in measurement – Take to nearest cm.
• Arm span – measuring length of one arm and doubling is incorrect – must ensure that everybody follows same method of measurement for consistency measure horizontal distance from left to right index finger.

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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