Moving means

1. Moving means

2. 3-mean smoothing • The first and last y-value are omitted • For all others, the y-values are replaced with the average of itself, the value above and the value below

3. 5-mean smoothing • The first two and last two y-values are omitted • For all others, the y-values are replaced by the average of itself, the two values above and the two values below

4. example • For the data below, find the: • 3-mean smoothed value for y = 4 • 3-mean smoothed value for y = 6 • 5-mean smoothed value for y = 4 • 5-mean smoothed value for y = 6

5. a) b) c) d) Cannot be calculated (this term is omitted)

6. 2-mean smoothing • When dealing with an even number such as 2, the problem becomes more difficult because the averages will not be symmetrical. • To get around this problem, we must take a 2-moving mean of the resultant averages (in other words, do the process twice). This is called centring. • This will become more clear with an example

7. Example (2-mean smoothing) • Apply 2-mean smoothing with centring to the following data:

8. First we leave spaces between each row of data. In each of these spaces we average the y-value above and the y-value below • This is shown on the next slide

10. Now we must centre our data. Each month should have a value above it and a value below it (except Jan and Jul, which are omitted) • We average these values above and below to get the smoothed, centred values

12. Example (4-mean smoothing) • For the same data set, apply 4-mean smoothing with centring. • In this case, the first two and last two values are omitted (see next slide)

14. Plotting on the CAS • Enter the data into a Lists&Spreadsheets page

16. Questions • Ex 7B All questions