Measures of Dispersion (With Diagram) | Biostatistics

After reading this article you will learn about the measures of dispersion which is designed to state numerically the extent to which in­dividual observation vary in the average.

Range:

It is the difference between the largest and smallest observation.

Range = Maximum value — Minimum value.

Mean Deviation:

Mean deviation is the arithmetic mean of absolute deviation from mean or any other specified value.

Mean deviation = ∑fd/n = ∑f(x – x̅)/n

x = specified value,

x̅ = mean value,

f = frequency,

n = total number of obser­vations.

Variance:

Variance is a measure of variation and is the sum of square of deviation (d) divided by the number of degree of freedom (n — 1).

Variance of the sample S² = ∑fd²/(n – 1)

It is also denoted by σ².

Standard Deviation:

A statistical measuring the spread or variability of the sample around the mean or in other words it may be defined as the measure of dispersion of different variables around the central value.

It is square root of variance:

Coefficient of Variation:

Standard deviation expressed as percentage of the mean and is denoted by the formula:

Coefficient of Mean Deviation:

Coefficient of mean deviation is used to compare variability among two series whose average differ widely and is denoted by the formula:

Standard Error:

It is the measure of the variation of the means. From standard error we can analyze how the sample mean (x̅) is related to the mean of the population (µ) and is given by the formula

SE = σ/√n.

Solved Problem:

Find out mean, standard deviation, mean deviation, coefficient of variation and standard error from the given sample: