Question

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

Answer 1

Since the number of months is even (12), we can equally divide the given data into two equal parts and obtain the averages of the first six months and last six months

In Year 2010	Sales (in tones)	Average
Jan	280	`(280 + 240 + 270 + 300 + 280 + 290)/6` = 276.667
Feb	240
Mar	270
Apr	300
May	280
Jun	290
Jul	210	`(210 + 200 + 230 + 200 + 230 + 210)/6` = 213.33
Aug	200
Sep	230
Oct	200
Nov	230
Dec	210

Thus we obtain semi-average I = 276.667 and semi-average II = 213.333

To fit a trend line we plot each value at the mid-point (month) of each half.

i.e we plot 276.667 in the middle of March and April

we plot 213.333 in the middle of September and October.

We join the two points by a straight line.

This is the required line.