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.

Year1972197319741975197619771978
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

Solution:

Method of Free Hand Curve
YearValueTotalMeanTrend Value
19722493  2200
19732638  2550
19742699  2950
1975303823338033403340
19763745  3650
19774079  4050
19784688  4499

MCQs Intermediate Mathematics Part-I Quadratic Equations

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