Moving means

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# Moving means - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Moving means' - vevina

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Presentation Transcript

### 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
• For all others, the y-values are replaced by the average of itself, the two values above and the two values below
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

a)

b)

c)

d) Cannot be calculated (this term is omitted)

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)
• Apply 2-mean smoothing with centring to the following data:

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

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)
• 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
• Enter the data into a Lists&Spreadsheets page
Questions
• Ex 7B All questions