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 the $x$-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 (Free Hand Curve)

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

Demerits (Free Hand Curve)

  • 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 from 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

MCQs Intermediate Mathematics Part-I Quadratic Equations

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