I am investigating the difference in growth rates between boys and girls across Year 7 to 11 in Mayfield High School. I have obtained the data from an electronic database and is therefore secondary data.

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Zilia D’Mello        Page         Statistics Coursework

Introduction

I am investigating the difference in growth rates between boys and girls across Year 7 to 11 in Mayfield High School. I have obtained the data from an electronic database and is therefore secondary data. I took a representative sample of 250 pupils from the database to carry out the investigation.

I am going to investigate the following hypotheses:

  • The height of the females will increase from Year 7 to 11.
  • The height of the males will increase from Year 7 to 11.
  • The weight of the females will increase from Year 7 to 11.
  • The weight of the males will increase from Year 7 to 11.
  • Females tend grow earlier then males.
  • The distribution of each male and female height in each year group is symmetrical and normal.
  • The distribution of each male and female weight in each year group is symmetrical and normal.

In order to carry out the investigation I will need to collect the following information: Year Group, Surname, Forename, Gender, Height and Weight. I can find this information from the database provided. I know that this information is reliable because it is based on a real school. The sample of pupils that I will take will be obtained through use of stratified and random sampling to ensure a true representative population.

Sampling

I reduced the population down to 250 pupils firstly by using stratified sampling. This ensure that the numbers of pupils of each gender and year group were in ratio to the actual population. The numbers of pupils of each gender and year group are shown in the table below.

I then obtained this sample of 250 pupils from the database through use of random sampling.I did this by using a calculator:

                Ran #        x    No of Pupils

e.g.         Year 7 Boys:        Ran #        x     32

The sample of 250 can be found in Appendix A.

Box and Whisker Plots

In order to draw the box and whisker diagrams I had to find the range, upper quartile, lower quartile and median of each set of data. This data was then drawn onto a diagram on which the length represented the range of the data and the box created in the middle by the quartiles in the middle represented the interquartile range. I had to find the outliers by multiplying the interquartile range by 1.5 and then adding this to the upper quartile and subtracting it from the lower quartile. Any numbers outside of this were considered outliers and marked onto the diagram as crosses. They were disregarded from the range.

I drew the box and whisker diagrams in order to find the data that was not representative of the population. These were the outliers. The diagrams also enabled me to see any trends or patterns within growth rates. It was possible to see how medians differed and also how interquartile ranges changed.

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The box and whisker diagrams can be found in Appendix B.

Outliers

I was able to decide whether or not to accept or reject an outlier by looking at the Body Mass Index which considers both the height and weight. This told me whether or not the outlier was ‘normal’. In order to be ‘normal’ the Body Mass Index had to lie between 15 and 25. The Body Mass Index is found by:

                        Weight   (kg)

                        Height²   (m)

Height

Females

Yr 7:

  • There were no outliers.

Yr 8:

  • 135cm – I have ...

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