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प्रश्न
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 |
सारिणी
योग
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उत्तर
Step 1: Understanding the 4-Yearly Centered Moving Average
A 4-yearly moving average is calculated by taking the average of four consecutive years’ index values. Since we have an even number of years, the average is centered between the second and third years of each group.
Step 2: Calculate 4-Year Moving Averages
| Years | Index | 4-Year Moving Sum |
4-Year Moving Average |
| 1976 | 0 | ||
| 1977 | 2 | ||
| 1978 | 3 | 0 + 2 + 3 + 3 = 8 | `8/4 = 2.0` |
| 1979 | 3 | 2 + 3 + 3 + 2 = 10 | `10/4 = 2.5` |
| 1980 | 2 | 3 + 3 + 2 + 4 = 12 | `12/4 = 3.0` |
| 1981 | 4 | 3 + 2 + 4 + 5 = 14 | `14/4 = 3.5` |
| 1982 | 5 | 2 + 4 + 5 + 6 = 17 | `17/4 = 4.25` |
| 1983 | 6 | 4 + 5 + 6 + 7 = 22 | `22/4 = 5.5` |
| 1984 | 7 | 5 + 6 + 7 + 10 = 28 | `28/4 = 7.0` |
| 1985 | 10 | - | - |
Step 3: Calculate Centered Moving Averages
| Year | Trend Value |
| 1978 | `(2.00 + 2.50)/2` = 2.25 |
| 1979 | `(2.50 + 3.00)/2` = 2.75 |
| 1980 | `(3.00 + 3.50)/2` = 3.25 |
| 1981 | `(3.50 + 4.25)/2` = 3.88 |
| 1982 | `(4.25 + 5.50)/2` = 4.88 |
| 1983 | `(5.50 + 7.00)/2` = 6.25 |
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