Method of Free-Hand Curve

It is familiar concept, briefly described for drawing frequency curves. In case of a time series a scatter diagram of the given observations is plotted against time on the horizontal axis and a freehand smooth curve is drawn through the plotted points. The curve is so drawn that most of the points concentrate around the curve, however, smoothness should not be scarified in trying to let the points exactly fall on the curve. It would be better to draw a straight line through the plotted points instead of a curve, if possible. The curve fitted by this method eliminates the short term and long term oscillations and the irregular movements from the time series and elevate the general trend. After having drawn such a curve or line the trend values or the estimated $Y$ values, which may be denoted by $Y$, can be read from the graph corresponding to each time period.

Once of the major disadvantage of this method is that different individual would draw curves or lines which would differ in slope and intercept and hence no two conclusions would be identical. The trend values so obtained will differ from individual to individual. However, it is the most simple and quickest method of isolating the trend. This method is generally employed in such situation where the scatter diagram of the original data conforms to some well define trend.

Example: Measure the trend by method of freehand curve from the given data of production of wheat in a particular area of the world.

 Years 1981 1982 1983 1984 1985 1986 1987 1988 1989 Production Million Metric Tons 6.6 6.9 5.6 6.3 8.4 7.2 7.2 8.5 8.5

Solution:

We observe that the graph of the original data does not show any closeness to any type of curve. It looks like increasing very slowly in straight (linear) manner. Thus we draw a line $AB$ as an approximation to the original graph. The line $AB$ represents the trend line and from this we read the trend values for the given years.