# 'The relationship between age and height'.

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Introduction

Maths Coursework

Mayfield high School is a school for students aged 11 to 16. It is a growing school so the number of students in each year varies. Although fictional the data is based on a real school.

A summary of the data given:

Year | Boys | Girls | Total |

7 | 151 | 131 | 282 |

8 | 145 | 125 | 270 |

9 | 118 | 143 | 261 |

10 | 106 | 94 | 200 |

11 | 84 | 86 | 170 |

The line of enquiry I wish to investigate is: ‘The relationship between age and height’

I will start off my extracting all the relevant information needed from the database. Then I will filter the data so that I have boys and girls of different year groups in different databases. I intend on giving each record a number and then using the random button on a calculator to select a random sample. I do this by pressing SHIFT and RAN and then multiplying by the total number of data. I then rounded the number which was my selected pupil. I filtered the information so that I could obtain a range of results from both genders and across all age groups. In total I selected a sample of 30. I did this because 30 is a large enough amount to obtain accurate results from and isn’t too large to work with. 30 is also exactly divides into 360 which will enable me to draw pie charts easier.

Highlighted (in yellow) here on the register are the 30 students I have chosen to analyse.

I have extracted the 30 students from the database and recorded their height, weight, gender and age in a table.

Middle

60

25

Male

16

1.52

60

26

Male

17

1.68

56

27

Male

16

1.62

48

28

Female

17

1.60

48

29

Female

17

1.65

52

30

Female

16

1.52

48

A bar chart showing the frequency of the ages to the nearest year

My bar shows that my randomly chosen sample of 30 pupils consists mainly of 14 year olds and not many 17 year olds.

I have extracted the randomly selected 30 students from the database and recorded their height, weight, gender and age in a table. I have given each pupil a number allowing me to extract further information easily.

I have represented my data as cumulative frequency charts. The first chart shows the age and the second chart shows the height.

A Cumulative frequency graph of the ages to the nearest year

A Cumulative frequency chart of the height (m)

The bar chart suggests that the modal age for students is 14.

The evidence from my sample suggests that at Mayfield High School there are likely to be fewer people who are taller than 180 cm.

Extending my information

To extend my investigation I will be looking at the relationship between age and height between girls and boys. To extend my line of enquiry I will be testing out the hypothesis:

‘In general, the older the person the taller that person is likely to be’

A New Sample

To extend the difference between boys and girls, I will need to take a new sample.

Conclusion

Boys only:

Girls only:

Combined sample:

These equations can be used to make predictions of height when one knows the height. For example, to predict the height of a 13 year old boy:

All the heights in the data are rounded to the nearest cm, so I should round this value to the nearest centimeter.

Using the equation of my lines of best fits, I can predict that a boy aged 13 is approximately 161cm tall.

The line of best is a best estimation of relationship between age and height. There are exceptional values in my data (such as the boy who is 206cm tall) which fall outside the general trend. The line of best fit is a continuous relationship, though age is a discrete variable. Rounding ages and heights to the nearest whole number makes my predictions less accurate.

Cumulative frequency can be a very powerful tool when comparing different data sets. This table shows the cumulative frequency for ages for boys, girls and for the mixed sample.

The best way of representing this information on a diagram is to draw cumulative frequency curves. If the curves are drawn on the axis, it is easier to compare the results.

Cumulative frequency curves for ages

The curves clearly show the trend towards higher age amongst boys and girls. However the curve is a continuous measure of cumulative frequency, and ages is a discrete variable. Cumulative frequency curves would be more appropriate when using heights.

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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