# Data Handling - Height and Foot Length

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Introduction

DATA HANDLING COURSEWORK

Plan

A former year10 class collected the data I will be using a few years ago. All of the students in each of the year 7 tutor groups had their height and foot length measured in centimetres. However, ‘7Q’ were out of school on a trip. Therefore, their data was not recorded.

I will use various methods to prove my hypothesis. These include cumulative frequency curves, box and whisker diagrams, histograms and stem and leaf diagrams. As well as the traditional mean, median, mode and range techniques.

I will firstly conduct the handling by collecting my data. I will do this via the technique of random sampling. I’ll do this by typing 148 (amount of data entries) then the #RAN key on my calculator. This will generate a random number between 0 and 148.

Middle

167.5

1

167.5

170 < h < 175

172.5

0

0

175 < h < 180

177.5

1

177.5

TOTALS

30

4516.5

Mean

4516/30 = 150.5cm

Median

30/2 = 15

145 + ((4/6) x 5) = 148.3cm

Mode

Modal class = 145 < h < 150

Range

177 – 138 = 39cm

CUMULATIVE FREQUENCY

MALE HEIGHT (CM) | FREQUENCY | CUMULATIVE FREQUENCY |

140 < h < 145 | 11 | 11 |

145 < h < 150 | 8 | 11 + 8 = 19 |

150 < h < 155 | 5 | 19 + 5 = 24 |

155 < h < 160 | 4 | 24 + 4 = 28 |

160 < h < 165 | 2 | 28 + 2 = 30 |

Lower quartile = 143cm

Upper quartile = 153.5cm

Inter quartile range = 9.5cm

FEMALE HEIGHT (cm) | FREQUENCY | CUMULATIVE FREQUENCY |

135 < h < 140 | 4 | 4 |

140 < h < 145 | 7 | 4 + 7 = 11 |

145 < h < 150 | 6 | 11 + 6 = 17 |

150 < h < 155 | 2 | 17 + 2 = 19 |

155 < h < 160 | 5 | 19 + 5 = 24 |

160 < h < 165 | 4 | 24 + 4 = 28 |

165 < h < 170 | 1 | 28 + 1 = 29 |

170 < h < 175 | 0 | 29 + 0 = 29 |

175 < h < 180 | 1 | 29 + 1 = 30 |

Lower quartile = 142.7cm

Upper quartile = 158.5cm

Inter quartile range = 15.8cm

Random Male Foot Length MMMR

FOOT LENGTH (cm) | MID POINT | FREQUENCY | MID POINT X FREQEUNCY |

20 | 20 | 1 | 20 |

21 | 21 | 2 | 42 |

22 | 22 | 6 | 132 |

23 | 23 | 7 | 161 |

24 | 24 | 5 | 120 |

25 | 25 | 8 | 200 |

26 | 26 | 1 | 26 |

TOTALS | 30 | 701 |

Mean

701/30 = 23.4cm

Median

30/2 = 15

23 + ((6/7) x 1) = 23.9cm

Mode

23cm

Range

26 – 20 = 6cm

Random Female Foot Length MMMR

FOOT LENGTH (cm) | MID POINT | FREQUENCY | MID POINT X FREQUENCY |

19 | 19 | 1 | 19 |

20 | 20 | 2 | 40 |

21 | 21 | 3 | 63 |

22 | 22 | 7 | 154 |

23 | 23 | 9 | 209 |

24 | 24 | 4 | 96 |

25 | 25 | 3 | 75 |

26 | 26 | 0 | 0 |

27 | 27 | 1 | 27 |

TOTALS | 30 | 683 |

Mean

683/30 = 22.8cm

Median

30/2 = 15

23 ((2/9) x 1) = 23.2cm

Mode

23cm

Range

27 – 19 = 8cm

After analysing my random sampled data, I have proved my hypothesis’ validity.

However, to clarify my results I will extend my analysis. I will change various variables this time. The sampling will be altered to systematic and the amount of data will be reduced to 15 pieces per gender. I will also exchange histograms for stem and leaf diagrams, but I will still use cumulative frequency curves.

Systematic Sampling

MALE NUMBER | HEIGHT (cm) | FOOT LENGTH (cm) |

5 | 156 | 23 |

15 | 161 | 25 |

25 | 141 | 21 |

35 | 143 | 23 |

55 | 154 | 25 |

65 | 147 | 24 |

70 | 151 | 26 |

75 | 148 | 23 |

80 | 155 | 22 |

85 | 150 | 23 |

90 | 144 | 22 |

100 | 138 | 23 |

120 | 144 | 22 |

125 | 149 | 22 |

130 | 167 | 25 |

Conclusion

15/2 = 7.5

145 + ((4.5/5) x 5) = 149.5cm

Mode

145 < h < 150

Range

162 – 140 = 22cm

CUMULATIVE FREQUENCY

MALE HEIGHT (cm) | FREQUENCY | CUMULATIVE FREQUENCY |

135 < h < 140 | 1 | 1 |

140 < h < 145 | 4 | 1 + 4 = 5 |

145 < h < 150 | 4 | 5 + 4 = 9 |

150 < h < 155 | 3 | 9 + 3 = 12 |

155 < h < 160 | 1 | 12 + 1 = 13 |

160 < h < 165 | 1 | 13 + 1 = 14 |

165 < h < 170 | 1 | 14 + 1 = 15 |

Lower quartile = 143.4cm

Upper quartile = 153.6cm

Inter quartile range = 10.2cm

FEMALE HEIGHT (cm) | FREQUENCY | CUMULATIVE FREQUENCY |

135 < h < 140 | 1 | 1 |

140 < h < 145 | 2 | 1 + 2 = 3 |

145 < h < 150 | 5 | 3 + 5 = 8 |

150 < h < 155 | 1 | 8 + 1 = 9 |

155 < h < 160 | 5 | 9 + 5 = 14 |

160 < h < 165 | 1 | 14 + 1 = 15 |

Lower quartile = 146.cm

Upper quartile = 157cm

Inter quartile range = 11cm

Systematic Male Foot Length MMMR

FOOT LENGTH (cm) | MID POINT | FREQUENCY | MID POINT X FREQUENCY |

21 | 21 | 1 | 21 |

22 | 22 | 4 | 88 |

23 | 23 | 5 | 115 |

24 | 24 | 1 | 24 |

25 | 25 | 3 | 76 |

26 | 26 | 1 | 26 |

TOTALS | 15 | 349 |

Mean

349/15 = 23.3cm

Median

15/2 = 7.5

23 + ((2.5/5) x 1) = 23.5cm

Mode

23cm

Range

26 – 21 = 5

Systematic Female Foot Length MMMR

FOOT LENGTH (cm) | MID POINT | FREQUENCY | MID POINT X FREQUENCY |

21 | 21 | 2 | 42 |

22 | 22 | 2 | 44 |

23 | 23 | 8 | 184 |

24 | 24 | 2 | 48 |

25 | 25 | 1 | 25 |

26 | 26 | 0 | 0 |

TOTALS | 15 | 343 |

Mean

343/15 = 22.9cm

Median

15/2 = 7.5

23 + ((3.5/8) x 1) = 23.4cm

Mode

23cm

Range

25 – 21 = 4

Evaluation

The hypothesis I predicted at the planning stages of my data handling coursework (stated above) was confirmed several times during the course of my analysis. Mean and mode displayed the traditional and easy-to-see confirmation. Whilst the cumulative frequency curves, histograms and steam and leafs methods showed the distribution of data and other specific trends.

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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