# My GCSE Coursework asks me to analyse a set of pre written data. I will need to include various diagrams and graphs all linked with comments and observations. The data I will be analysing is the heights and weights of a group of children.

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Introduction

Victoria Newsum

## GCSE Maths/Statistics Coursework

## Aim

My GCSE Coursework asks me to analyse a set of pre written data. I will need to include various diagrams and graphs all linked with comments and observations. The data I will be analysing is the heights and weights of a group of children. The number of children I analyse will be my choice.

## Hypothesis

I think that the taller the person is, the heavier they will weigh.

### Method

As there are too many people in the year group I will take a sample of pupils from the year group. Firstly I will number all the males from 001-151 and the females from 001-131.

I have decided to use a sample of 80 pupils from the year group. I will be using stratified sampling to work out how many males and females I will be using as there are more males than females so to get a fair proportion of the year group I will need to take a larger proportion of males than females.

Once I know how many males and how many females I will be using I will use the random number generator on my calculator to pick the students at random.

I will then put their heights and weights into a table.

To work out how many males and females I will be using I need to work out the overall total number of pupils in the year group.

151 + 131 = 282

To work out the number of males and females I will be taking I need to use the stratified sampling method

### Number of males = 151 / 282 x 80 = 43

### Number of females = 131 / 282 x 80 = 37

Now I know the number of males and females I will be using I can use the random number generator on my calculator to select the pupils.

Middle

This scatter diagram shows a positive correlation between the height and weight for males. It proves my hypothesis was right.

I have drawn a line of best fit in the diagram so I can use it to estimate any other heights or weights if I need to.

I have shown:

- The sample heights and weights for the males
- Grouped frequency table for the male heights
- Pie chart to represent the distribution of male heights
- Mean, mode, median, upper quartile, lower quartile and interquartile range for the male heights
- Grouped frequency table for the male weights
- Pie chart to represent the distribution of male weights
- Mean, mode, median, upper quartile, lower quartile and interquartile range for the male weights
- Scatter diagram to show the correlation between the male heights and weights

I am now going to list the height and weight data for the females:

##### Females

Now I have got my sample heights and weights for the females, I will put them into two grouped frequency tables, one for height, and one for weight, then I will work out the mean, mode, median, upper quartile, lower quartile and inter quartile range, and produce a scatter diagram to show the correlation.

Here is the height one:

Here is a pie chart showing the distribution of the height results:

I will now work out the mean, mode, median, upper quartile, lower quartile and interquartile values for the male weights using the table above the pie chart.

To work out the mean height I will use this formula:

Σfx

#### Σf

= 56.265

37

Mean = 1.5206756676 (1.52)

To work out the modal weight I have to find out which group has the highest frequency:

Mode = 1.50 – 1.59

The median weight can be worked out by using a cumulative frequency graph.

Conclusion

Median = 46

To work out the lower quartile I will find out what 1/4 of the total c.f is and do the same as the c.f but with this number.

Lower quartile = 42

To work out the upper quartile I will find out what 3/4 of the total c.f and do the same as the c.f but with this number.

Upper quartile = 50

To work out the interquartile range I will take the final number of the lower quartile from the final number of the upper quartile. This gives me the inter quartile range.

Interquartile range = 8

Now I have worked out the mean, mode, median, upper quartile, lower quartile and interquartile range for the female and male weights. I will do a scatter graph to show the correlation between the heights and weights to see if my hypothesis that the taller the person the higher the weight was correct.

This scatter diagram shows a positive correlation between the height and weight for males and females. It proves my hypothesis was right.

I have drawn a line of best fit in the diagram so I can use it to estimate any other heights or weights if I need to.

I have shown:

- Grouped frequency table for the female and male heights and weights
- Pie chart to represent the distribution of female and male heights and weights
- Mean, mode, median, upper quartile, lower quartile and interquartile range for the female and male weights and heights
- Grouped frequency table for the female and male weights and heights
- Pie chart to represent the distribution of female and male heights and weights
- Mean, mode, median, upper quartile, lower quartile and interquartile range for the female and male heights and weights
- Scatter diagram to show the correlation between the female and male heights and weights

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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