Q.5 (A) (i) Obtain the 4-yearly centered moving averages for the following data:
| Years | 1971 | 1972 | 1973 | 1974 | 1975 | 1976 |
|---|---|---|---|---|---|---|
| Production | 1 | 0 | 1 | 2 | 3 | 2 |
| Years | 1977 | 1978 | 1979 | 1980 | 1981 | 1982 |
|---|---|---|---|---|---|---|
| Production | 3 | 6 | 5 | 1 | 4 | 10 |
Best answer
Answer: 1.25, 1.75, 2.25, 3, 3.75, 3.875, 3.875, 4.5 for the years 1973 to 1980
4-yearly moving totals are placed between the 2nd and 3rd years of each group; pairs of consecutive totals are then added (centred) and divided by 8.
| Year | Production | 4-yearly moving total | 2-period moving total (centred) | 4-yearly centred moving average |
|---|---|---|---|---|
| 1971 | 1 | |||
| 1972 | 0 | |||
| 4 | ||||
| 1973 | 1 | 10 | 1.25 | |
| 6 | ||||
| 1974 | 2 | 14 | 1.75 | |
| 8 | ||||
| 1975 | 3 | 18 | 2.25 | |
| 10 | ||||
| 1976 | 2 | 24 | 3.00 | |
| 14 | ||||
| 1977 | 3 | 30 | 3.75 | |
| 16 | ||||
| 1978 | 6 | 31 | 3.875 | |
| 15 | ||||
| 1979 | 5 | 31 | 3.875 | |
| 16 | ||||
| 1980 | 1 | 36 | 4.50 | |
| 20 | ||||
| 1981 | 4 | |||
| 1982 | 10 |
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