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.
| Year | 1972 | 1973 | 1974 | 1975 | 1976 | 1977 | 1978 |
| No. of Accidents | 2493 | 2638 | 2699 | 3038 | 3745 | 4079 | 4688 |
- 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:
| Year | Value | Total | Mean | Trend value |
|---|---|---|---|---|
| 1972 | 2493 | 2200 | ||
| 1973 | 2638 | 2550 | ||
| 1974 | 2699 | 2950 | ||
| 1975 | 3038 | 233380 | 3340 | 3340 |
| 1976 | 3745 | 3650 | ||
| 1977 | 4079 | 4050 | ||
| 1978 | 4688 | 4499 |
The method of free hand curve is useful for:
- 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.
- Visual Communication: It also helps to present trends in the data in a clear and easily understandable way for non-statistical audiences.
- 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
