Moving-Averages gcse Edexcel

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Exam code:1ST0

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

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)

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