Investigate whether boys are bigger than girls.

Statistics Coursework

Aim

In this coursework, I want to investigate whether boys are bigger than girls. I have to take into consideration weight and age, as this will affect the height. A boy of 16 years old will, almost certainly, be taller than a girl of 11 years old. I will split the data into age groups to combat this problem and compare data of pupils in the same year. The data I am using is from Mayfield School and Ridgewood School. I want to see whether pupils have a growth spurt in a certain year and if shorter people are generally heavier than taller people. I want to investigate this because it is a very interesting subject that, I believe, hasn’t been looked into before.

Hypothesis

I think that boys will be taller than girls. I think that boys will have more spread out data than girls and that boys will have their growth spurts in years 9-10 However, I think that girls will have less spread out data apart from year 9, when I think that girls will have their growth spurts.

Plan

I am going to carry out my investigation by looking at 2 sets of data. The first set is Mayfield School, this is secondary data. There are 1183 pupil’s data, including height, year group, weight and gender. In the Ridgewood data I have 396 pupils data, including height, gender and year group. This is primary data. If I collect data myself, primary data, then I know how it has been collected, however, this could be very times consuming and expensive.

The Mayfield data is secondary data, which has already been collected for me. Secondary data is good to use because it would cut out collecting it. I do not know how it has been collected though and could be biased.

I am going to collect 59 pieces of data in my sample. This is enough to represent the population but isn’t too much data to deal with.

I will sample from every year group in the Ridgewood School data.

I will use random systematic sampling to obtain data from each year without being bias. Systematic sampling is when a regular pattern is used to choose the sample. Every item in the population is listed, a starting point is randomly chosen and then every nth item is selected. I used this type of sampling because it is quick and simple. However, it would be unrepresentative of the population if a pattern existed in the list, but upon inspection there isn’t a pattern. I will put the year 9, 10 and 11 girls in order of height, pick a starting point and pick every 5 pieces of data. These are some types of sampling I didn’t use.

Stratified Sampling

Stratified sampling is when the population is divided into categories (strata) by age, gender, social class, etc. Then, a random sample is chosen from each category. The size of each sample is in proportion to the size of each category within the population

Cluster Sampling

This is when the population is divided into groups or clusters. A random sample of clusters is chosen and every item in the chosen cluster is surveyed. I didn’t use this type of sampling because, if I chose a small number of large clusters, it would be unrepresentative of the population.

Quota Sampling

Quota sampling is when instructions are given concerning the amount (quota) of each section of the population to be sampled.

A disadvantage is that the actual people or items chosen are left to the discretion of the surveyor, which could lead to bias.

An advantage of this method is that no sampling frame is required.

Convenience Sampling

As it says in the name, this is the most convenient way of sampling. For example, if you need a sample of sixty people, it could be the first sixty people you meet.

It is highly likely that this sample would be biased and unrepresentative.

Opinion Polls

Large-scale opinion polls often use a combination of cluster and quota sampling.

An example of this is the accurate estimates of the outcome of general election for public office.

The sample size may be large but is often based on a very small proportion of the population.

To ensure my results are meaningful, after I have got my sample from the data, I will compare it to a larger source of data. I will compare my Ridgewood results to Mayfield data, to make sure it is reliable and it is a representative of the whole. If, after I have sampled my stratified Ridgewood data, there is an incorrect piece of data, for example, the pupil being 10 foot high, which is obviously wrong, I will not use that pupils data and pick another.

I will present my data in 6 tables. Year 9, gender and height. Year 10, gender and height, and so on. I will need two tables for each year, boys and girls. If I use a box plot and whisker diagram for each year, having a scale at the bottom of my page, this would make it very easy to compare the spread and trends of the data from year to year.

Presentation of Data & Calculations