Moving Averages (Edexcel GCSE Statistics)

Revision Note

Moving Averages

What are moving averages?

  • A moving average is the average of a number of successive observations

    • This makes it easier to spot trends in data that varies cyclically or seasonally

  • The number of data points included in each average must cover one complete cycle

    • Usually this will mean one complete year

  • A four-point moving average is the most common moving average

    • e.g. for a year divided into four quarters or into four seasons

  • To calculate moving averages

    • e.g. for a four-point moving average with 8 data points

      • the first moving average is the mean of the first four data points

      • the second moving average is the mean of the 2nd through 5th data points

      • the third moving average is the mean of the 3rd through 6th data points

      • the fourth moving average is the mean of the 4th through 7th data points

      • the fifth (and last) moving average is the mean of the 5th through 8th data points

    • Note that the group of data points for each moving average overlaps the group before and after it

    • Stop when you can no longer get a ‘full group’ for the next average

      • e.g. four points for a four-point moving average

How do I plot moving averages on a time series graph?

  • It is useful to plot moving averages onto a time series graph

    • This makes it easier to draw accurate trend lines

  • Each moving average should be plotted at the midpoint of the time intervals it covers

    • e.g. for a four-point moving average

      • the average for the first 4 points will be plotted halfway between the 2nd and 3rd points

      • the average for the 2nd through 5th points will be plotted halfway between the 3rd and 4th points

      • etc.

  • You should not join up the points for moving averages

Examiner Tips and Tricks

  • Remember not to join up the moving average points on a time series graph

    • This is different from the data points, which are joined up

Worked Example

The following table records the number of visitors to Wayne’s World of Widgets for 2021, 2022 and the first two quarters of 2023:

Year

2021

2022

2023

Quarter

1

2

3

4

1

2

3

4

1

2

Visitors

(thousands)

6.2

8.5

8.8

7.6

6.2

8.9

9.6

7.9

6.8

9.5


This data is also represented on the following time series graph:

Time series graph for data in the question


Calculate the four-point moving averages for this data and plot them on the time-series graph.


The first moving average will be the mean of the first 4 data points (i.e. the 4 quarters of 2021)

Remember, to find the mean add the values together and divide by the number of values

fraction numerator 6.2 plus 8.5 plus 8.8 plus 7.6 over denominator 4 end fraction equals 7.775


The next moving average will be the mean of the next group of 4 data points (i.e. quarters 2, 3 and 4 of 2021 and quarter 1 of 2022)

fraction numerator 8.5 plus 8.8 plus 7.6 plus 6.2 over denominator 4 end fraction equals 7.775


Continue this process to find all 7 moving averages

fraction numerator 8.8 plus 7.6 plus 6.2 plus 8.9 over denominator 4 end fraction equals 7.875

fraction numerator 7.6 plus 6.2 plus 8.9 plus 9.6 over denominator 4 end fraction equals 8.075

fraction numerator 6.2 plus 8.9 plus 9.6 plus 7.9 over denominator 4 end fraction equals 8.15

fraction numerator 8.9 plus 9.6 plus 7.9 plus 6.8 over denominator 4 end fraction equals 8.3

fraction numerator 9.6 plus 7.9 plus 6.8 plus 9.5 over denominator 4 end fraction equals 8.45


Now plot these on the time series graph

Remember, these need to be plotted at the midpoint of the time intervals each one covers

So the first point will be halfway between quarters 2 and 3 of 2021

The second point will be halfway between quarters 3 and 4 of 2021

And so on

Also remember not to join these moving average points up!

Time series graph with four point moving averages plotted

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Roger B

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Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

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