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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 |
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.
APPEARS IN
संबंधित प्रश्न
State the uses of time series
Define secular trend
Define seasonal index
State the different methods of measuring trend
Compute the average seasonal movement for the following series
| Year | Quarterly Production | |||
| I | II | III | IV | |
| 2002 | 3.5 | 3.8 | 3.7 | 3.5 |
| 2203 | 3.6 | 4.2 | 3. | 4.1 |
| 2004 | 3.4 | 3.9 | 37 | 4.2 |
| 2005 | 4.2 | 4.5 | 3 | 4.4 |
| 2006 | 3.9 | 4.4 | 4.2 | 4.6 |
The following table gives the number of small-scale units registered with the Directorate of Industries between 1985 and 1991. Show the growth on a trend line by the free hand method.
| Year | No. of units (in '000) |
| 195 | 10 |
| 986 | 22 |
| 1987 | 36 |
| 198 | 62 |
| 1989 | 55 |
| 1990 | 0 |
| 1991 | 34 |
| 1992 | 50 |
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
Calculate the seasonal indices from the following data using the average method:
| Year | I Quarter | II Quarter | III Quarter | IV Quarter |
| 2008 | 72 | 68 | 62 | 76 |
| 2009 | 78 | 74 | 78 | 72 |
| 2010 | 74 | 70 | 72 | 76 |
| 2011 | 76 | 74 | 74 | 72 |
| 2012 | 72 | 72 | 76 | 68 |
Choose the correct alternative:
The additive model of the time series with the components T, S, C and I is
The sum of the series `log_4 2 - log_8 2 + log_16 2 + ...............` to `oo` is
