This document describes the method of semi-averages for measuring secular trends in data. The method involves dividing the data into two equal halves and calculating the arithmetic mean of each half. While simple to understand and apply, the method assumes a straight line relationship between data points and the trend line may change with additional data. The method is explained for both even and odd datasets.

1. Free Hand curve Method

3. METHOD OF SEMI-AVERAGE

4. METHOD OF SEMI-AVERAGE
This method is as simple and relatively objective as the free hand
method. The data is divided in two equal halves and the arithmetic mean
of the two sets of values.

5. Advantages
• This method is simple to understand as compare to other methods for
measuring the secular trends.
• Everyone who applies this method will get the same result.

6. Disadvantages
• The method assumes a straight line relationship between the plotted points
without considering the fact whether that relationship exists or not.
• If we add more data to the original data then we have to do the complete
process again for the new data to get the trend values and the trend line also
changes.

7. Explanation of the Method
• When data is even: In this case, the time series will be into two parts
and then we calculate the average of each part. Suppose if we have 10
years data then we divide it into 5 -5 years and then we will calculate
the first five-year average and the next five-year
• When data is odd: In this case, we just leave the middle data and we
will follow the above-said procedure for the rest.

10. Fit a trend line by the method of semi-averages for
the given data.