What is standard deviation?

It is the measure of spread in a data.


The standard deviation is usually denoted with the letter σ (lower case sigma). It is defined as the square root of the variance.

A simple example

Suppose we wished to find the standard deviation of the set of the numbers 4 and 8.

Step 1: find the arithmetic mean (or average) of 4 and 8,

(4 + 8) / 2 = 6.

Step 2: find the deviation of each number from the mean,

4 − 6 = − 2

8 − 6 = 2.

Step 3: square each of the deviations (amplifying larger deviations and making negative values positive),

( − 2)² = 4

2² = 4.

Step 4: sum the obtained squares (as a first step to obtaining an average),

4 + 4 = 8.

Step 5: divide the sum by the number of values, which here is 2 (giving an average),

8 / 2 = 4.

Step 6: take the non-negative square root of the quotient (converting squared units back to regular units),

So, the standard deviation is 2.