Maths open box

By Lev Murynets

Statistics coursework

Introduction

In this assignment I will be investigating and comparing student data concerning Mayfield high school the two hypotheses below to see whether they are correct

I believe that in most cases the taller the student is, the more they would weigh, due to the taller person having a larger BMI, although there may be acceptions to the rule this is commonly the case.

In order to prove this hypothesis I will look for a trend between the height and weight of assorted students from Mayfield School’s 1183 pupils with the help of scatter diagrams to analyse whether there is a correlation between the height and weight across year 10 and 11, eliminating all other data that is unneeded to find this result

I believe that in most cases male students are taller than females in year 11, this may not be the case in lower year groups, in the later stages of puberty males tend to be taller than females, but the lower year groups will most probably have different results as puberty occurs at different times for different people

This will be tested in a number of graphs comparing the results of the height to weight ratio for year 7’s with the ratio for year 11’s

The data provided it too diverse to give an efficient reading, and testing all 1183 individuals will prove unnecessarily time consuming, an acceptable sum of pupils to use would be 10% of the pupils, as this would give a sample large enough to avoid anomaly and small enough to be time efficient, and represent the school to use in the tests to prove the two hypothesis mentioned above

10% of 1183 is 118.3, rounded to 118 students; these will be taken accordingly from each year group to accurately give a proportion of that particular year group

Graph A

I will have to decide a way to select the students of that year group, with 10% of that year group’s girls and 10% of that year groups boys represented accordingly, for this I can use one of the three following methods of sampling

Random Sampling
Stratified sampling
Systematic sampling

The data for Mayfield School is already divided by year group, so it would be more sensible to use stratified sampling shown in the graph above (graph A)

In accordance to the relevance of the data, the male and female percentages must also be equivalent to 10% of girls in the year group

So out of year 11’s 170 pupils is broken down into male and female (Stage 1)

Stage 1

Then broken down further to the 10% require for testing (stage 2)

Stage 2

Further Random selection of the 10% from the category provided (year 7 males) gives a random list of numbers between 0 and 151 enabling to choose 15 completely random choices for the 10% required

Using the following template to create this random number generator

The Selected few whose number was selected go into the table and the rest are deleted

Year Seven Female

Here I have shown the year 7 selected at random females in order, and their names, surnames height detail and weight detail, as well as a table below

The graph below clearly shows a strong positive correlation between height and weight in this particular year group

For this graphs line of best fit, I found the mean of the data (1.59,44), and drew the line from that point dividing the results so that the amounts on both sides are equal

The graph below clearly shows a strong positive correlation between height and weight in this particular year group although it is much more scattered than previous results

For this graphs line of best fit, I found the mean of the data (1.56, 46), and drew the line from that point dividing the results so that the amounts on both sides are equal

Below are the chosen statistics of the year 9 chosen males showing height weight surname and forename

The graph below shows the weak ...