Page 305 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Year Population (in million)

1990 412
1991 438
1748
1992 444 = 437
4
1993 454
1994 470
1995 482
1942
1996 490 = 485.5
4
1997 500

Solution: The average of the first four years is 437 and that of the last four years 485.5. These
two points shall be taken corresponding to the middle periods, i.e., 1 July, 1991 and
st
1 July, 1995.
st
The estimate of population for 1998 by projecting the semi-average trend line is 514
million. The actual figure given to us is 520 million. The difference is due to the fact
that time series analysis helps us to get the best possible estimates on certain
assumptions which may come out to be true or not depending upon how far those
assumptions have been realised in practice.

Trend by the Method of Semi-Averages

520
514
510

500
490
480
470 TREND LINE
460

450
440
ACTUAL
430 DATA

420
410
1990 1991 1992 1993 1994 1995 1996 1997 1998
YEARS

Example 5: The sale of a commodity in tonnes varied from January 1997 to December 1997 in the
following manner :

280 300 280 280 270 240

230 230 220 200 210 200
Fit a trend line by the method of semi-averages.

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