# mayfield course work -boys are generally heavier than girl. This has to do with their body structure. Therefore I predict that my results will produce a pattern which shows that boys weight more than girls.

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Introduction

Chioma Akunna Mathematics Coursework: Statistics

11 Beatrice

Introduction

In this coursework I will be looking at various lines of enquiry based on data collected from Mayfield High School. Therefore I will be doing an investigation into the relationship between height, weight, body mass index and age of boys and girls at this school.

People’s height and weight are affected by their age and gender.

I assume that in year 7-9, more girls would be taller than boys. This is because girls tend to grow faster than boys at the early stages of development but boys eventually grow taller than them. Therefore in year 10-11, more boys would be taller than girls. This also applies to the adults aged 20 and above.

As for the weight, boys are generally heavier than girl. This has to do with their body structure. Therefore I predict that my results will produce a pattern which shows that boys weight more than girls. This pattern will be produced for all age groups: 7-9, 10-11 and 20+. The scatter diagram will have no correlation between age and BMI. This is because the data being used is non-continuous as age group 17-19 has been skipped in this investigation.

The histogram for year group 7-11 will show that most of the students will be underweight but more girls would be overweight than boys. As for the adults aged 20 and above, most of them will be overweight.

Method

There are 1183 students in Mayfield but I need to sample only 60 students. The population has been divided into strata according to their year group and gender too.

Middle

0

Male

1.82

80

24.2

10

39

7

Male

1.83

90

26.9

11

39

3

Male

1.75

81

26.4

14

27

10

Male

1.78

70

22.1

18

27

7

Male

1.78

65

20.5

19

41

2

Male

1.74

89

29.4

PIE CHART: The pie charts will be used to show the relationship between height and age group. The result will then compared between boys and girls of the different age groups.

11 – 14 years: Male Female

Height Interval (m) | Tally | Frequency | Angle | Tally | Frequency | Angle | |

1.4 – 1.49 | || | 2 | 34 | |||| | | 6 | 108 | |

1.5 – 1.59 | |||| | 4 | 69 | |||| | 5 | 90 | |

1.6 – 1.69 | |||||||| || | 12 | 206 | |||| || | 7 | 126 | |

1.7 – 1.79 | ||| | 3 | 51 | | | 1 | 18 | |

1.8 – 1.89 | | | 1 | 18 |

15 – 16 years: Male Female

Height Interval (m) | Tally | Frequency | Angle | Tally | Frequency | Angle | |

1.5 – 1.59 | || | 2 | 80 | || | 2 | 72 | |

1.6 – 1.69 | ||| | 3 | 120 | |||| | 5 | 180 | |

1.7 – 1.79 | || | 2 | 80 | || | 2 | 72 | |

1.8 – 1.89 | | | 1 | 40 | | | 1 | 36 | |

1.9 – 1.99 | | | 1 | 40 | 36 |

20+ Male Female

Height Interval (m) | Tally | Frequency | Angle | Tally | Frequency | Angle | |

1.50 – 1.54 | | | 1 | 36 | ||||

1.55 – 1.59 | | | 1 | 36 | ||||

1.60 – 1.64 | || | 2 | 72 | ||||

1.65 – 1.69 | |||| | 4 | 144 | ||||

1.70 – 1.74 | | | 1 | 36 | ||||

1.75 – 1.79 | |||| | 5 | 180 | || | 2 | 72 | |

1.8 – 1.84 | ||| | 3 | 108 | ||||

1.85 – 1.89 | | | 1 | 36 |

With reference to table 1, the median group and estimated mean in the sample were higher for boys than for girls. However the sample for girls in year group 7-9 were more spread out with a range of 0.49m compared to 0.39m for the boys. This must have affected the mean. The evidence from the sample suggests that in year group 7-9, 12 boys out of 41 pupils, have a height between 1.6m and 1.69m whilst 7 girls out of the same 41 pupils have a height of 1.6m and 1.69m. This prove that the first part of my hypothesis is wrong: i predicted that in year 7-9, more girls would be taller than boys but my result shows more boys to be taller than girls.

However in year group 10-11, there were more girls than boys with a height between 1.6m and 1.69m though the samples for boys were more spread out with a range of 0.49m compared to 0.39 for the girls. Once again my hypothesis is wrong because i predicted that in year 10-11, boys would be taller than girl.

These conclusions are based on a sample of only 60 pupils. Therefore the limitation of data could have affected the accuracy of my hypothesis. If I could extend the sample my hypothesis is likely to be right.

MEASURES OF AVERAGES

Heights

Year group 7 - 9: Male Female

Height Interval (m) | Frequency f | Midpoint x | fx | Frequency f | Midpoint x | fx |

1.4 – 1.49 | 2 | 1.445 | 2.89 | 6 | 1.445 | 8.69 |

1.5 – 1.59 | 4 | 1.545 | 6.18 | 5 | 1.545 | 7.725 |

1.6 – 1.69 | 12 | 1.645 | 19.74 | 7 | 1.645 | 11.515 |

1.7 – 1.79 | 3 | 1.745 | 1.745 | 1 | 1.745 | 1.745 |

1.8 – 1.89 | 1 | 1.845 | 1.845 | |||

∑f = 21 | ∑fx = 34.045 | ∑f = 20 | ∑fx = 31.52 |

Estimated mean = 34.045 = 31.52

21 20

= 1.62 = 1.57

Year group 10 - 11 Male Female

Height Interval (m) | Frequency f | Midpoint x | fx | Frequency f | Midpoint x | fx |

1.5 – 1.59 | 2 | 1.545 | 3.09 | 2 | 1.545 | 3.09 |

1.6 – 1.69 | 3 | 1.645 | 4.935 | 5 | 1.645 | 8.225 |

1.7 – 1.79 | 2 | 1.745 | 3.49 | 2 | 1.745 | 3.49 |

1.8 – 1.89 | 1 | 1.845 | 1.845 | 1 | 1.845 | 1.845 |

1.9 – 1.99 | 1 | 1.945 | 1.945 | |||

∑f = 9 | ∑fx = 15.305 | ∑f = 10 | ∑fx = 16.65 |

Estimated mean = 15.305 = 16.65

9 10

= 1.70 = 1.67

20+ Male Female

Height Interval (m) | Frequency f | Midpoint x | fx | Frequency f | Midpoint x | fx |

1.54 – 1.54 | 1 | 1.52 | 1.52 | |||

1.55 – 1.59 | 1 | 1.57 | 1.57 | |||

1.6 – 1.64 | 2 | 1.62 | 3.24 | |||

1.65 – 1.69 | 4 | 1.67 | 6.68 | |||

1.7 – 1.74 | 0 | 1.72 | 0 | 1 | 1.72 | 1.72 |

1.75 – 1.79 | 2 | 1.77 | 3.54 | 5 | 1.77 | 8.85 |

1.8 – 1.84 | 3 | 1.82 | 5.46 | |||

1.85 – 1.89 | 1 | 1.87 | 1.87 | |||

∑f = 10 | ∑fx = 16.55 | ∑f = 10 | ∑fx = 17.452 |

Estimated mean = 16.55 = 17.452

10 10

= 1.66 = 1.75

Table 1

Measures of average: heights (metres)

Estimated Mean | Median Group | Modal Group | Range | |

Year group 7-9 male female | 1.62 | 1.6 – 1.69 | 1.6 – 1.69 | 0.39 |

1.57 | 1.5 – 1.59 | 1.6 – 1.69 | 0.49 | |

Year group 10-11 male female | 1.70 | 1.6 – 1.69 | 1.6 – 1.69 | 0.49 |

1.67 | 1.6 – 1.69 | 1.6 – 1.69 | 0.39 | |

20+ male female | 1.66 | 1.65 – 1.69 | 1.65 – 1.69 | 0.29 |

1.75 | 1.75 – 1.79 | 1.75 – 1.79 | 0.19 |

CUMULATIVE FREQUENCY: the cumulative frequency graph will be used to compare the boys and girls weight in each age group. I will be commenting on the inter-quartile range and median and making reference to the box plot.

Year group 7-9 Male Female

Weight Interval (kg) | Tally | Frequency | Cumulative Frequency | Tally | Frequency | Cumulative Frequency |

30 – 39 | | | 1 | 1 | | | 1 | 1 |

40 – 49 | |||||||||| | 12 | 13 | |||||||| | | 11 | 12 |

50 – 59 | ||||| | 6 | 19 | |||| | | 6 | 18 |

60 – 69 | | | 1 | 20 | || | 2 | 20 |

70 – 79 | 0 | 20 | ||||

80 - 89 | | | 1 | 21 |

Year group 10 - 11: Male Female

Weight Interval (kg) | Tally | Frequency | Cumulative Frequency | Tally | Frequency | Cumulative Frequency |

30 – 39 | | | 1 | 1 | |||

40 – 49 | || | 2 | 2 | ||| | 3 | 4 |

50 – 59 | ||| | 3 | 5 | |||| | 5 | 9 |

60 – 69 | ||| | 3 | 8 | | | 1 | 10 |

70 – 79 | 0 | 8 | ||||

80 – 89 | | | 1 | 9 |

20+ Male Female

Weight Interval (kg) | Tally | Frequency | Cumulative Frequency | Tally | Frequency | Cumulative Frequency |

40 – 49 | | | 1 | 1 | |||

50 – 59 | ||| | 3 | 4 | |||

60 – 69 | | | 1 | 1 | ||| | 3 | 7 |

70 – 79 | ||| | 3 | 4 | 7 | ||

80 – 89 | |||| | 5 | 9 | || | 2 | 9 |

90 – 99 | | | 1 | 10 | | | 1 | 10 |

Conclusion

- All three measures of average are higher for boys than for girls. In year group 7-9 the median and mode as a measure of average was similar. However, the data shows that boys weight more than girls in the same age group. Table 3 shows the estimated mean for boys in year group 10-11 to be 58.9kg and 50.5kg for girls in the same year group. The box plot shows that the girls’ inter-quartile range is 4.6kg less than the boys’. This suggests that the boys’ weights are more spread out than the girls. As for the adults all three measures of average are greater for the men than for the women. The adult data supports my hypothesis and proves that it is right.
- There is no correlation between body mass index and age both for the adult data and the sample. This is as a result of non-continuous data as age group 17-19 was skipped. This proves my hypothesis right.
- Histogram shows more than half of the sample (61%) to be underweight. This proves prediction right.
- Standard deviation for adult shows that male data is closer to mean than female data. With a standard deviation of 2.54, we can conclude that BMI values of male are close to the mean (24.89). On the other hand, female values are more spread out with a mean of 24.39 and a deviation of 4.71. This could be as a result of limited data.

Further sampling of data could make all my hypothesis correct. Therefore I could improve on the result obtained by extending the sample. It would give a wider range of data which could change the result obtained.

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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