Statistics

Averages

There are three measures of average: mean, median and mode.

Mean – is the most used measure of average.

To calculate the mean: you add all of the values together and divide it by the amount of values there are.

For example: Here are the scores out of 10, from a maths test: 5, 2 7, 4, 8, 1. Find the mean.

1. First, add up all of the values:
2. Then, .
3. The mean is .

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Median – To calculate the median, you have to put the values in order and then the middle number is the median value. If there are 2 middle numbers, then you find the mean of those two numbers.

To find the median value of this data set: 4, 3, 7, 1, 5

First, put them in order: 1, 3, 4, 5, 7

The middle number here is 4.

4 is the median.

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Mode – To calculate the mode, you have to find the number which is the most common in the data set.

Find the mode of this data set: 0, 1, 7, 5, 7, 4, 7

The most common number is 7. So 7 is the mode.

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Below is a summary diagram showing how to work out the different averages and the range.

There are three different types of average:

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Range – To calculate the range, you have to find the difference between the largest and smallest values.

To find the range of this data set: 13, 16, 27, 90, 1

89 is the range.

Comparing distributions

All of these methods are useful, but some are more useful than others depending on the scenario.

Finding the mean of a data set tends to be the best measure as it considers all of the values.

Representing data

Data can be represented using a bar chart, pie chart, scatter diagram, line graph, frequency diagram or a pictogram.

When deciding the graph/chart to use, you need to first look at the data that you want to represent.

• Continuous data – use line graphs
• Discrete data – use bar charts
• Percentages – use pie charts
• Two variables – use scatter diagrams

Also, once you have decided the graph to use don’t forget SALT

S = Scale        A = Axes        L = Labels      T = Title

Bar charts:

The height of the bar tells us the frequency of the data. So, the vertical axis is labelled ‘Frequency’.

Line graphs:

Line graphs can show us trends over time. A straight line is used to join up the plots.

Pictograms:

Pictures are used to show data. It is essential for a ‘key’ to be used to show us what each picture represents.

Pie charts:

These are circular shape and are divided into different sizes to usually show fractions.

Remember, a circle = 360°

Drawing a pie chart: first work out the fraction of the total of that segment, then convert it to an angle and draw this on the chart.

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For example

Grade	A	B	C	D	E
Frequency	7	11	6	4	2

We need to work out the angle that each of these represent. So, if we look at Grade E. The frequency is 2 out of 30 in total. So, we can write that as . Next, multiply it by 360°. °

You do this for each of the Grades and draw the angle on the pie chart accurately.

Frequency diagrams/polygons:

These are useful for comparing sets of data. You can join up the tops of the charts with straight lines.

Scatter diagrams:

These show the relationship between two variables. The link between the variables can also be known as correlation.

You can have a positive correlation, negative correlation or no correlation.

Positive correlation – when one variable increases, the other also increases

Negative correlation – when one variable increases, the other decreases

No correlation – there is no relationship between the variables

The lines drawn through the points is called the line of best fit. The line does not have to go through all of the points or through the origin, it is just useful to show the trend. This line cannot be drawn if there is no correlation.