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.

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

Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

You may also like...

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

x Logo: Shield Security
This Site Is Protected By
Shield Security