## Unit 18 Section 5 : Trends
Moving averages can be used to make predictions. They do this by smoothing out monthly, seasonal or other periodic variations.
For example, an ice-cream seller might expect to sell more in the summer than he does in the winter.
He could use a moving average over the four seasons to find out if his sales are increasing for each 12 month period. ## Example Question(a) Calculate the 4 point moving averages for this list of data:6 5 7 4 6.1 5.1 7.1 4.1
The first 4 point moving average is calculated using the mean of the first 4 items of data:
For the second 4 point moving average we discard the first value (6) and include the next value (6.1) like this:
The next three 4 point moving averages are calculated in a similar fashion: The 4 point moving averages for this list of data are: 5.5, 5.525, 5.55, 5.575, 5.6 (b) Estimate the next two values in the list.
Looking at the moving averages so far (showing them to 3 decimal places), we can see that they increase by 0.025 each time:
If we call the next value in the list
Now we have predicted that the next value after 4.1 will be 6.2, and that the 7th moving average should be 5.650. Our predictions for the next two values in the list are 6.2 and 5.1.
## Practice QuestionWork out the answer to each part of the question then click to see whether you are correct.
The table below gives the average daytime temperatures for each of the four seasons over a two-year period.
(a) Start by calculating the first five moving averages:
The differences between the moving averages are:
(b) What is the mean of the four differences between the moving averages? To predict the 6th and 7th moving averages we need start with the 5th moving average and add this value on twice.
(c) What are the predictions for the 6th and 7th moving averages? Now we can use the same method as in the first example to predict Spring and Summer temperatures for Year 3.
(d) What is the predicted temperature for Spring in Year 3
(e) What is the predicted temperature for Summer in Year 3
## ExercisesWork out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.
You have now completed Unit 18 Section 5
Produced by A.J. Reynolds April 2011 |