The Method of Free Hand Curve (2020)

Introduction to Free Hand Curve

The Method of Free Hand Curve is a simple and non-mathematical technique used to fit a curve to a set of data points by visually estimating the trend. It provides a quick, approximate visualization of the relationship between variables.

It is used to

• Plot Data Points: Scatter plot the data points on a graph.
• Draw Curve: Using a smooth, freehand line, draw a curve that best represents the overall trend of the data points.
• No Rigid Rules: The curve is drawn based on the analyst’s judgment, without strict mathematical formulas.

Exploring Data Patterns

This method is subjective and less precise than mathematical curve-fitting techniques but is useful for initial data exploration or when data patterns are irregular.

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.

Practical Example of Curve

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 usefulness of the Method of Free Hand Curve

The method of freehand curve is useful for:

1. Exploratory Data Analysis (EDA): As a preliminary step free 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.

Real-Life Examples of Free-Hand Curve

Some real-life examples where the Method of Free Hand Curve can be applied:

• Economics:
  • Plotting and estimating trends in stock market prices over time.
  • Visualizing the relationship between inflation and unemployment rates.
• Meteorology:
  • Drawing temperature trends over days or months based on scattered weather data.
  • Estimating rainfall patterns over a year.
• Education:
  • Plotting student performance trends over semesters to identify improvements or declines.
  • Visualizing the relationship between study hours and exam scores.
• Healthcare:
  • Tracking a patient’s blood pressure or glucose levels over time to observe trends.
  • Estimating the progression of a disease based on irregular data points.
• Business:
  • Visualizing sales trends over months or years to identify seasonal patterns.
  • Estimating the relationship between advertising expenditure and revenue growth.
• Sports:
  • Plotting an athlete’s performance metrics (e.g., running speed, scores) over time to observe trends.
  • Visualizing the relationship between training hours and performance improvement.

Summary

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. The freehand curve provides a quick, intuitive way to understand trends or relationships without relying on complex mathematical models.

MCQs Intermediate Mathematics Part-I Quadratic Equations