MEASURES OF DISPERSION | STANDARD DEVIATION

STANDARD DEVIATION

The concept of Standard Deviation was introduced in 1893 by Karl Pearson. It is the most commonly used measure of dispersion.

A standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

Standard deviation can be defined as the positive square root of the arithmetic mean of the squares of the deviation of the given observation from their arithmetic mean, i.e., it is ‘root mean square deviation from mean’.

 

For example

Calculate standard deviation from the following observation

10, 9, 13, 20, 8, 10, 20, 8, 10, 12

 

Solution:

Values x	x²
10	100
9
13
20
8
10
20
8
10
12
Total x = 120	Total x² = 1622

 

n = 10

sum x² = 1622

sum x = 120

σ = square root of Sum x²/ n – (sum x/n) ²

= square root of 1622/10 – (120/10) ²

= square root of 162.2 – 144

= square root of 18.2

= 4.27