i) Method of Least Square: - This method is most commonly used
method of measuring trend. It is a mathematical method and a trend line is
fitted to the data in such a manner that the following two conditions are
satisfied:-
i) The sum
of deviation of the actual values from their respective mean is zero.
ii) The
sum of square of the deviations of the actual and compute values is least from
this line. That is why this method is called method of least square.
The
straight line trend is represented by the equation:
Y
= a + bx
Where, y =
denotes the trend values
a
= represents the intercept on y axis.
b=
represents slope of the trend line.
Merits:-
i) This is
a mathematical method of measuring trend.
ii) Trend
values can be obtained for all the given time periods in the series.
Demerits:-
i) This
method is more tedious and time consuming.
ii) This
method cannot be used to fit the growth curves.
ii) Semi-average method: - Under
this method, the given data is divided into two parts. After that an average of
each part is obtained which gives two points. Each 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 which gives the required trend line.
Merits:-
i) This
method is simple to understand as compared to the moving average method and the
method of least square.
ii) This
is an objective method of measuring trend as everyone who applies this method
gets the same result.
Demerits:-
i) It is
affected by extreme values.
ii) This
method assumes straight relationship between the plotted points whether this
exist or not.
iii) Method of moving average: - Under
this method the average value for a certain time span is secured and this
average is taken as the trend value for the unit of time falling at the middle
of the period covered in the calculation of the average. While using this
method it is necessary to select a period for moving average.
Merits:-
i) This
method is simple to understand and apply.
ii) It is
particularly effective if the trend of a series is very irregular.
iii) It is
a flexible method of measuring trend because all figures are not changed if a
few figures are added to the data.
Demerits:-
i) Trend
values cannot be computed for all years.
ii) No
there is no hard and fast rule for selecting the period of moving average.
iii) This
method is not appropriate if the trend situation is not linear.