1 of 8 0-day streak

Select and compare smoothing methods

Question 1 of 8

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A water authority records daily demand in a district. This table shows the response recorded at each period. The purpose is to reduce the effect of one unusually large or small observation while keeping the longer-term movement visible. Use the shortest candidate window, which covers 3 periods

The observations are recorded in consecutive periods
Period	Observed value (ML)
1	174
2	173
3	175
4	174
5	175
6	176
7	199
8	181
9	180
10	182
11	184

(a)1 mark

Which smoothing choice best meets this purpose? The purpose is to reduce the effect of one unusually large or small observation while keeping the longer-term movement visible. Use the shortest candidate window, which covers 3 periods

Use the 5-term moving median (takes the middle response in each window)

Use the 3-term moving median (takes the middle response in each window)

Use the 3-term moving mean (averages all responses in each window)

(b)1 mark

How many smoothed values are retained by the 3-term moving median? Give an integer

Number of retained values Format: integer

Which statement best compares the raw observations with the smoothed series?

The selected 3-term moving median reduces the isolated extreme, and the overall increasing direction remains visible (raw endpoints 174 and 184; smoothed endpoints 174 and 182)

A wider window retains more values at the ends and is therefore preferable for this purpose

The smoothed series has a value at every raw period because endpoint windows can be shortened (there are 11 raw observations)