The Method of Free Hand Curve

The secular trend is measured by the method of the free-hand curve in the following steps:

• Take the time periods along $x$-axis by taking appropriate scaling
• Plot the points for observed values of the $Y$ variable as the dependent variable against the given time periods
• Join these plotted points by line segments to get a historigram
• Draw a free hand smooth curve (or a straight line) through the histogram

In this method we draw the given times series data on graph paper, then we draw a free hand trend line through the plotted graph according to the trend of the graph. Then we read trend values from this free-hand trend line.

It is generally preferred to use a curve instead of a straight line to show the secular trend.

Merits:

• The free-hand curve method is a simple, easy, and quick method for measuring secular trends.
• A well-fitted trend line (or curve) gives a close approximation to the trend based on a mathematical model.

Demerits:

• It is a rough and crude method.
• It is greatly affected by personal bias as different persons may fit different trends to the same data.
  The estimates are not reliable due to personal bias.

Question: The following time series shows the number of road accidents in Punjab for the year 1972 to 1978.

Year	1972	1973	1974	1975	1976	1977	1978
No. of Accidents	2493	2638	2699	3038	3745	4079	4688

• Obtain the historigram showing the number of road accidents and a free hand trend line by drawing a straight line
• Find the trend values for this time series

Solution:

Year	Value	Total	Mean	Trend Value
1972	2493			2200
1973	2638			2550
1974	2699			2950
1975	3038	233380	3340	3340
1976	3745			3650
1977	4079			4050
1978	4688			4499