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# Maths GCSE Statistics Coursework

Extracts from this document...

Introduction

Introduction

I have been asked to compare 173 year 7 pupils and 178-year 11 pupils who were asked to estimate the length of a bamboo stick to the nearest centimetre, which was held horizontally not vertical. I am going to investigate the two different age groups to see who had the more constant guesses from the secondary data, I have been given. The actual length of the bamboo stick is 1.58 metres. As 351pieces of data would be too big to sample, I am going to random sample 50 pieces of the data for each year. Not to be biased I am going to stratify my data to keep the boys and girls in proportion.

Hypothesis 1

I predict that the ability to accurately guess the length of the bamboo stick will increase

Middle

136

M

1.38

140

F

1.67

143

M

1.23

148

F

1.58

151

M

1.35

153

M

1.50

159

F

1.80

163

M

2.12

165

M

1.75

168

M

1.95

Year 7 Grouped Frequency chart

 Length (cm) Tally Frequency 0 < L < 1.0 2 1.00 < L < 1.2 2 1.20 < L < 1.4 13 1.40 < L < 1.6 18 1.60 < L < 1.8 8 1.80 < L < 2.0 5 2.00 < L < 2.2 2

Year 11 Sampled Data

 Pupil Gender Length (cm) 3 M 1.66 9 M 1.50 15 F 1.61 18 F 1.60 19 F 1.65 21 M 1.60 22 M 1.60 26 M 1.60 27 F 1.50 37 M 1.50 41 M 1.30 44 M 1.56 51 M 1.77 52 M 1.85 54 M 1.90 57 F 1.85 63 M 1.69 68 F 2.00 69 F 2.00 74 F 1.45 78

Conclusion

2.00

170

M

1.12

171

M

1.35

177

F

1.90

Year 11 grouped frequency chart

 Length (cm) Tally Frequency 1.0 < L < 1.2 2 1.20 < L < 1.4 9 1.40 < L < 1.6 13 1.60 < L < 1.8 17 1.80 < L < 2.0 5 2.00 < L < 2.2 4

Year 7 mean

As the data is big I have grouped it into frequency table.

 Length (cm) Mid point Frequency MP × F 0 < L < 1.0 0.5 2 1 1.00 < L < 1.2 1.1 2 2.2 1.20 < L < 1.4 1.3 13 16.9 1.40 < L < 1.6 1.5 18 27 1.60 < L < 1.8 1.7 8 13.6 1.80 < L < 2.0 1.9 5 9.5 2.00 < L < 2.2 2.1 2 4.2 Total 50 74.4

Mean = Total (MP × Frequency)

Total frequency

Mean = 74.4 = 1.488 cm

50

Year 11 mean

 Length (cm) Mid point Frequency MP × F 1.0 < L < 1.2 1.1 2 2.2 1.20 < L < 1.4 1.3 9 11.7 1.40 < L < 1.6 1.5 13 19.5 1.60 < L < 1.8 1.7 17 28.9 1.80 < L < 2.0 1.9 5 9.5 2.00 < L < 2.2 2.1 4 8.4 Total 50 80.2

Mean = 80.2 = 1.604 cm

50

Mini Conclusion

Mean year 7 = 1.488 cm

Mean year 11 = 1.608 cm

The actual length of the bamboo stick is 1.58 metres.

My mean shows that my hypothesis was right, that year 11’s overall guess would be closer to the actual length of the bamboo stick than the overall guess of year 7. Also my mean shows that year 7 had more extreme values.

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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