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प्रश्न
Find the trend of production by the method of a five-yearly period of moving average for the following data:
| Year | Production ('000) |
| 1979 | 126 |
| 1980 | 123 |
| 1981 | 117 |
| 1982 | 128 |
| 1983 | 125 |
| 1984 | 124 |
| 1985 | 130 |
| 1986 | 114 |
| 1987 | 122 |
| 1988 | 129 |
| 1989 | 118 |
| 1990 | 123 |
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उत्तर
Computation of five-yearly moving averages
| Year | Production ('000) |
5-Yearly centred moving total |
5-Yearly moving averages |
5-Yearly centred moving averages |
| 1979 | 126 | - | - | - |
| 1980 | 123 | - | - | - |
| 1981 | 117 | 619 | 123.8 | |
| 123.6 | ||||
| 1982 | 128 | 617 | 123.4 | |
| 124.1 | ||||
| 1983 | 125 | 624 | 124.8 | |
| 124.5 | ||||
| 1984 | 124 | 621 | 124.2 | |
| 123.6 | ||||
| 1985 | 130 | 615 | 123 | |
| 123.4 | ||||
| 1986 | 114 | 619 | 123.8 | |
| 123.2 | ||||
| 1987 | 122 | 613 | 122.6 | |
| 121.9 | ||||
| 1988 | 129 | 606 | 121.2 | |
| 1989 | 118 | - | - | - |
| 1990 | 123 | - | - | - |
The last column gives the trend in the production by the method of the five-yearly period of moving average.
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संबंधित प्रश्न
Define secular trend
Explain cyclic variations
The annual production of a commodity is given as follows:
| Year | production (in tones) |
| 1995 | 155 |
| 1996 | 162 |
| 1997 | 171 |
| 19988 | 182 |
| 1999 | 158 |
| 2000 | 880 |
| 2001 | 178 |
Fit a straight line trend by the method of least squares
Determine the equation of a straight line which best fits the following data
| Year | 2000 | 2001 | 2002 | 2003 | 2004 |
| Sales (₹ '000) | 35 | 36 | 79 | 80 | 40 |
Compute the trend values for all years from 2000 to 2004
The sales of a commodity in tones varied from January 2010 to December 2010 as follows:
| In Year 2010 | Sales (in tones) |
| Jan | 280 |
| Feb | 240 |
| Mar | 270 |
| Apr | 300 |
| May | 280 |
| Jun | 290 |
| Jul | 210 |
| Aug | 200 |
| Sep | 230 |
| Oct | 200 |
| Nov | 230 |
| Dec | 210 |
Fit a trend line by the method of semi-average
Use the method of monthly averages to find the monthly indices for the following data of production of a commodity for the years 2002, 2003 and 2004
| 2002 | 2003 | 2004 |
| 15 | 20 | 18 |
| 18 | 18 | 25 |
| 17 | 16 | 21 |
| 19 | 13 | 11 |
| 16 | 12 | 14 |
| 20 | 15 | 16 |
| 21 | 22 | 19 |
| 18 | 16 | 20 |
| 17 | 18 | 1 |
| 15 | 20 | 16 |
| 14 | 17 | 18 |
| 18 | 15 | 20 |
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Least square method of fitting a trend is
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