# The Method of Free Hand Curve (2020)

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.

• 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:

The method of free hand curve is useful for:

1. Exploratory Data Analysis (EDA): As a preliminary step free hand curve method helps us to understand the basic characteristics of the data and identify potential relationships between variables.
2. Visual Communication: It also helps to present trends in the data in a clear and easily understandable way for non-statistical audiences.
3. Limited Data: When you have a relatively small dataset, a free hand curve might be sufficient to get a basic idea of the central tendency.

By understanding the method of free hand curves and its limitations, one can use it as a valuable tool for initial data exploration and visualization alongside other statistical techniques for a more robust analysis.

MCQs Intermediate Mathematics Part-I Quadratic Equations