# There will be a positive correlation between height and weight.The spread of boys' height will be larger than the spread of girls' height

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Introduction

Mohamed Hassan student number: 20042512

GCSE

Mathematics Data Handling Coursework

Introduction

For my investigation I am using data from a simulated school called Mayfield High School. This is a mixed secondary school with 1183 people, split into 604 boys and 579 girls. There are five-year groups, from 7 to 11. This contains many different records, including, first name, surname, height, weight, age (decimal, years and months), month of birth, sex, hand, favourite sport subject and TV program, hours of TV, IQ, distance between home and school, means of travel to school, and Ks2 and Ks3 results. I have chosen to investigate the relationship between height and weight, because it is quite probable that they influence each other. Here are my hypotheses, which are all related to height, weight or both. : -

- There will be a positive correlation between height and weight.
- The spread of boys’ height will be larger than the spread of girls’ height.
- The average boys’ weight will be larger than the average girls’ weight.
- The older someone is the better the correlation is between height and weight.

I will collect data on the height and weight of 60 pupils. I will also collect the data on their age and gender. To make sure my data sample is fair and unbiased. I will do a random stratified sample, which means I will have an amount of records from each gender year group, in correlation to their percentage of the school size.

I will investigate these hypotheses by drawing an assortment of graphs and diagrams, and making several calculations.

Any data, which seems implausible, such as a height less than 1m, or larger than 2.2m, or a weight less than 20kg, or more than 90kg, I will discount, and randomly choose another pupil of the same year and gender. I will now explain my hypotheses in more detail.

1.

Middle

## Boys

## Girls

The cumulative frequency graph showed me that the boys and the girls both had quite a small inter quartile range (IQR), because the gradient was quite steep for the central 50% of the y axis. The boys’ lower quartile was 1.55 metres and their upper quartile was 1.7 metres, meaning there was an IQR of 0.15 metres. The lower quartile of the girl’s data was 1.545 metres and the upper quartile was 1.68 metres, meaning there was an IQR of 0.135 metres. So the boys inter quartile range was larger than the girl’s inter quartile range, proving my hypothesis correct.

But, the minimum girls height was 1.2, and the maximum was 1.8, giving a range of 0.6, whereas the minimum boys height was 1.41 and the maximum boys height was 1.91, giving a range of 0.5, which is 0.1m lower than the girls, meaning that my hypothesis is incorrect, and the spread of the girls height is actually larger than the spread of the boys height. To make the minimum, maximum, IQR, and range data easier to understand, I have drawn box and whisker diagrams for the girls and boys heights on the same axis.

I will now investigate the standard deviation of the girls and boys height, which will be another indication as to whether the girls’ or the boys’ data has a larger spread. Standard deviation is the square root of the mean of the square of the deviation from the mean. To do this I will need to find the mean height, and subtract it from the mid class value for each group. The equation for standard deviation is

Here are the standard deviation calculations

## Girls

0.7267/30=0.024223333

√0.024223333=0.15563847

## Boys

0.65465541/30=0.021821847

√0.021821847=0.147722195

These calculations show that the girls’ standard deviation is larger than the boys’ standard deviation, indicating that there is a higher spread of height for girls than for boys.

Conclusion

###### Evaluation

I think my project went well, and I have fulfilled my aims, to prove correct or incorrect my four hypotheses. But although my sample was large enough to come to a reasonable conclusion, as to whether my hypotheses were correct or incorrect, for my results to have been more foolproof, I think I should have had a larger sample, perhaps 100 pupils altogether, with 50 of either sex. For example I only had 8 pupils in year 11, whilst having 14 pupils in year7 and 8. Eight is quite a low number of data pints to plot a graph with, so to make my results more conclusive, I need more pupils. Because I need a stratified sample, to keep my pupil sample fair, the only way I can get more pupils in the higher year is to increase my total sample. So this was one of my limitations, that I did not have a big another sample to provide full proof results. I don’t think there was any bias in my results, because my sample was random, so there can’t have been any bias. I think my plan was very effective, because I went through it in order, and completed all of my graphs and calculations that I needed. To further my work, I could investigate other things which effect height and weight such as whether the pupil was left handed or right handed, and their IQ. One of my other limitations was grouping my data, because I did it with my data grouped, which meant my answer was only an estimate. So to improve my project, I could have done standard deviation for the height data, with the data ungrouped. So If I did the calculations with ungrouped data, my results would be more accurate.

©Mohamed Hassan

20-01-07

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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