Q.5 (B) (i) Obtain the trend value for the following data using 4-yearly centered moving averages :
| Years | 1976 | 1977 | 1978 | 1979 | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 |
|---|---|---|---|---|---|---|---|---|---|---|
| Index | 0 | 2 | 3 | 3 | 2 | 4 | 5 | 6 | 7 | 10 |
Best answer
Answer: Trend values 2.25, 2.75, 3.25, 3.875, 4.875, 6.25 for 1978 to 1983.
4-yearly moving totals are placed between the middle years; adding pairs of them gives centred totals, and dividing by 8 gives the centred moving averages (trend values).
| Year | Index | 4-yearly moving total | 2-period total (centred) | Trend value (÷ 8) |
|---|---|---|---|---|
| 1976 | 0 | |||
| 1977 | 2 | 8 (between 1977 and 1978) | ||
| 1978 | 3 | 10 (between 1978 and 1979) | 18 | 2.25 |
| 1979 | 3 | 12 (between 1979 and 1980) | 22 | 2.75 |
| 1980 | 2 | 14 (between 1980 and 1981) | 26 | 3.25 |
| 1981 | 4 | 17 (between 1981 and 1982) | 31 | 3.875 |
| 1982 | 5 | 22 (between 1982 and 1983) | 39 | 4.875 |
| 1983 | 6 | 28 (between 1983 and 1984) | 50 | 6.25 |
| 1984 | 7 | |||
| 1985 | 10 |
No trend values can be obtained for 1976, 1977, 1984 and 1985.
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