# Measures of Dispersion: Definition, Types, Pros & Cons

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## What is Measures of Dispersion?

Measures of dispersion or spread give us some idea of how the values of a distribution cluster around the average and to what extent the observations differ from the mean. The three main measures of dispersion of a distribution are the range, the variance and the standard deviation.

### The Range

The range (R) of a distribution is simply the difference between the two extreme items/observations. That is, it is the difference between the highest value and the lowest value. Usually, and in general, a small dispersion means a small range, while a large dispersion means a large range.

For example, the range (R) of this set of numbers 3,7,9 and 13 is 13-3 =10.

Xn = Highest value

X1 = Lowest value R = Xn – Xi

Xn = 13, Xi = 3

R = 13 – 3 = 10

• It is the simplest measure of dispersion.
• It is a reasonably good indication of spread.

• It is not a particularly good measure of spread because it is very difficult to interpret.
• It will be badly affected by just one extreme value. Care is therefore necessary when it is used.

### The Variance

The variance is simply the square of the standard deviation. By calculation, it is derived through the summation of the squares of the differences between each observation and the mean divided by the number of observations.

• It is not a sound mathematical index.
• [t exaggerates the dispersion of data by squaring their variations.

### Standard Deviation

The standard deviation is simply the square root of the variance. It is the most popular measure of spread.

• It is the most popular measure of dlspersion in a distribution.
• It is a good measure of dispersion since all the values are used in its computatlon.
• It is very important and useful in the analysis of t-test.
• It is most useful mathematically, especially for further statistical analysis.
• It has great practical utility in sampling and statistical inference.