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• Level: GCSE
• Subject: Maths
• Word count: 3480

# Present information on body measurements of year 10 and compare results to see if there are any patterns.

Extracts from this document...

Introduction

Maths CourseworkCharlotte Nellist

Our maths coursework is to present information on body measurements of year 10 and compare results to see if there are any patterns.  We took six measurements. These were:

• Height
• Arm Span
• Shoe Size
• Hand Span
• Hand Area

Height

Each pupil in the year had their height taken by other members of the group.  They stood with their heels touching the wall and the other person would take their height with a metre ruler. The height measurements were not accurate because some girls did not take off their shoes and many girls’ shoes have big heels.

Arm Span

All pupils were put in pairs and they measured the arm span against the wall, on the wall a metre was marked out.  They also used a metre ruler to measure the rest of the arm span.

Shoe Size

For this, instead of all the pupils measuring their feet with a ruler or finding the area of them, we just did it by shoe size.  Most people used UK measurements but some people used Euro measurements so I just changed it all to UK measurements.

Hand Span

For this, pupils took their own hand span themselves.  We did this by getting some squared paper and spreading our hand across the page as far as we could, and then we put a dot where the little finger was and then where the thumb was.  We then got a ruler and measured between the two dots, this gave us the hand span.

Middle

σ = 0.02

### Males

 x (x-x) (x-x)² 1.75 -0.01 0.0001 1.90 0.14 0.0196 1.65 -0.11 0.0121 1.70 -0.06 0.0036 1.80 0.04 0.0016 1.73 -0.03 0.0009 1.89 0.13 0.0169 1.76 0.00 0.00 1.69 -0.07 0.0049 1.78 0.02 0.0004 1.68 -0.08 0.0064 ∑(x-x)² = 0.0665

σ =   0.0665

11

=0.023443267

σ = 0.02

Group 1  Female  x 1.65                From the information on the left I can see the mean

σ 0.07        height of males is greater than the mean height of

Male     x 1.73                females, in all three groups.  This shows that males

σ 0.05        are taller than females, but I guessed that

Group 2  Female  x 1.67                anyway.  The standard deviation (σ) gives the spread

σ 0.02        of heights, in group 1 the females have a larger

Male     x 1.77                spread than the males and the same goes in group 2

σ 0.005        but in group 3 they are the same.

Group 3  Female x 1.59

σ 0.02

Male     x 1.76

σ 0.02

## Group 1 – Arm Span

This is the bottom maths group again and there are 10 females and 6 males in the group.  It is measured in metres again.

Females

x = (1.70+1.58+1.62+1.63+1.68+1.50+1.65+1.63+1.70+1.47)

10

= 16.16

10

= 1.616

x = 1.62m

Males

x = (1.55+1.56+1.73+1.95+1.60+1.74)

6

= 10.13

6

= 1.688333333

x = 1.69m

## Female

 x (x-x) (x-x)² 1.70 0.08 0.0064 1.58 -0.04 0.0016 1.62 0.00 0.00 1.63 0.01 0.0001 1.68 0.06 0.0036 1.50 -0.12 0.0144 1.65 0.03 0.0009 1.63 0.01 0.0001 1.70 0.08 0.0064 1.47 -0.15 0.0225 ∑(x-x)² = 0.1856

σ =   0.1856

10

= 0.043081318

σ = 0.04

## Males

 x (x-x) (x-x)² 1.55 -0.14 0.0196 1.56 -0.13 0.0169 1.73 0.04 0.0016 1.95 0.26 0.0676 1.60 0.09 0.0081 1.74 0.05 0.0025 ∑(x-x)² = 0.2684

σ =   0.2684

6

= 0.086345558

σ = 0.09

## Group 2 – Arm Span

This is the top group again there are 11 females and 11 males and it is still in metres.

Female

x = (1.54+1.61+1.61+1.50+1.55+1.65+1.71+1.61+1.55+1.62+1.63)                                                                       11

= 17.58

11

= 1.598181818

x = 1.60m

Males

x = (0.80+0.83+1.72+1.84+1.69+1.70+1.80+1.68+1.70+1.64+1.76)

11

= 17.16

11

x = 1.56m

#### Female

 X (x-x) (x-x)² 1.54 -0.06 0.0036 1.61 0.01 0.0001 1.61 0.01 0.0001 1.50 -0.1 0.01 1.55 -0.05 0.0025 1.65 0.05 0.0025 1.71 0.11 0.0121 1.61 0.01 0.0001 1.55 -0.05 0.0025 1.62 0.02 0.0004 1.63 0.03 0.0009 ∑(x-x)² = 0.0348

σ =   0.0348

11

= 0.016958871

σ = 0.02

Male

 x (x-x) (x-x)² 0.80 -0.76 0.5776 0.83 -0.73 0.5329 1.72 0.16 0.0256 1.84 0.28 0.0784 1.69 0.13 0.0169 1.70 0.14 0.0196 1.80 0.24 0.0576 1.68 0.12 0.0144 1.70 0.14 0.0196 1.64 0.08 0.0064 1.76 0.2 0.04 ∑(x-x)² = 1.389

Conclusion

The medians of the female’s arm spans are lowest 1.61m and highest 1.65m, with a difference of only 4cms.  Group 3 has the greatest range and group 1 has the greatest inter-quartile range.  The medians of the male’s arm spans are more spread out with the lowest at 1.65m and the highest at 1.73m, with a difference of 8cms.  Also the group 1 males have the largest range and the widest inter-quartile range.

The box and whisker graphs were very useful because they enabled me to see all six sets of results for the height on one piece of paper and also all six sets of results for arm span on another piece of paper.

From looking at both sets of graphs side by side, the group 1 males have the largest range in heights and also the largest range in arm spans.  Also looking at the rest of the results they are positioned in similar places on both graphs.

From this information I can also answer my question, ‘Is there a connection between height and arm span?’ and are people square? I can conclude that people are not square but that people’s height and arm span are proportional, so the taller people are the larger their arm span or the shorter people are the smaller their arm span.

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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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