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Moving means. 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. 5-mean smoothing. The first two and last two y-values are omitted

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3 mean smoothing
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
5 mean smoothing
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
example
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
slide5

a)

b)

c)

d) Cannot be calculated (this term is omitted)

2 mean smoothing
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
example 2 mean smoothing
Example (2-mean smoothing)
  • Apply 2-mean smoothing with centring to the following data:
slide8

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
slide10

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
example 4 mean smoothing
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)
plotting on the cas
Plotting on the CAS
  • Enter the data into a Lists&Spreadsheets page
questions
Questions
  • Ex 7B All questions