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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 |
तक्ता
बेरीज
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: Final Trend Values
The trend values, calculated as 4-yearly moving averages, are:
- 1978 → 2.0
- 1979 → 2.5
- 1980 → 3.0
- 1981 → 3.5
- 1982 → 4.25
- 1983 → 5.5
- 1984 → 7.0
Conclusion
The 4-yearly centered moving average smooths short-term fluctuations in the data and provides a clear trend pattern.
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