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.


  • 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.


  • 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.

No. of Accidents2493263826993038374540794688
  • 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


Method of Free Hand Curve
YearValueTotalMeanTrend Value
19722493  2200
19732638  2550
19742699  2950
19763745  3650
19774079  4050
19784688  4499