Semi Averages Method
When this technique is used the given data is divided into two parts, preferably with the same number of ears. For e.g. if we are given a data from 1992 to 2009 over a time-period of 18 years, the two equal parts will be each of nine years from 1992 to 2000 & from 2001 to 2009. In case of odd number of years such as 9, 13, 17, etc, two equal parts can be made simply by omitting the middle year. For e.g. if data are given for 19 years from 1991 to 2009 the middle year 2000 will be omitted.
After the data have been divided into two parts & average (arithmetic mean) of every part is obtained. We thus get two points. Every point is plotted at the mid-point of the class interval covered by the respective part and then the two points are joined by a straight line that gives the required trend line. The line can be extended downwards or upwards to get the intermediate values or to predict future values.
The following example shall illustrate this method as follows:
Illustration:
Fit a trend line to the following data by the method of semi-averages
|
Year
|
Sales of firm A (thousand units)
|
Year
|
Sales of firm A (thousand units)
|
|
2003
|
102
|
2007
|
108
|
|
2004
|
105
|
2008
|
116
|
|
2005
|
114
|
2009
|
112
|
|
2006
|
110
|
|
|
Solution:
Since seven years are given the middle year shall be left out and an average of the first three years and the last three years shall be obtained. The average of the first three years is
102 + 105 + 114 / 3 = 321/3 = 107
and the average of the last three years is
108 + 116 + 112/3 = 336/3 = 112.
Thus we get two points 107 & 112 which shall be plotted corresponding to their respective middle years 2004 & 2008. By joining these two points we obtain the required trend line. The line can be extended and can be used either for prediction or for determining the intermediate values.