Measures of Dispersion Meaning, Absolute and Relative

Measures of dispersion refer to statistical tools used to describe the spread or variability of a dataset. These measures help in understanding the extent to which data points differ from the central tendency (mean, median, or mode). Common measures of dispersion include:

• Range: The difference between the highest and lowest values.
• Variance: The average squared deviation of each data point from the mean.
• Standard deviation: The square root of variance, providing a more interpretable measure of spread.
• Interquartile range (IQR): The range between the 25th and 75th percentiles.

Characteristics of Measures of Dispersion:

• A measure of dispersion should be rigidly defined
• It must be easy to calculate and understand
• Not affected much by the fluctuations of observations
• Based on all observations

Classification of Measures of Dispersion

The measure of dispersion is categorized as:

(i) An absolute measure of dispersion:

• The measures which express the scattering of observation in terms of distances i.e., range, quartile deviation.
• The measure which expresses the variations in terms of the average of deviations of observations like mean deviation and standard deviation.

(ii) A relative measure of dispersion:

We use a relative measure of dispersion for comparing distributions of two or more data set and for unit free comparison. They are the coefficient of range, the coefficient of mean deviation, the coefficient of quartile deviation, the coefficient of variation, and the coefficient of standard deviation.

Coefficient of Dispersion

Whenever we want to compare the variability of the two series which differ widely in their averages. Also, when the unit of measurement is different. We need to calculate the coefficients of dispersion along with the measure of dispersion. The coefficients of dispersion (C.D.) based on different measures of dispersion are

• Based on Range = (X _max – X _min) ⁄ (X _max + X _min).
• C.D. based on quartile deviation = (Q₃ – Q1) ⁄ (Q₃ + Q1).
• Based on mean deviation = Mean deviation/average from which it is calculated.
• For Standard deviation = S.D. ⁄ Mean

Coefficient of Variation

100 times the coefficient of dispersion based on standard deviation is the coefficient of variation (C.V.).

C.V. = 100 × (S.D. / Mean) = (σ/ȳ ) × 100