Sample Standard Deviation

In statistics, we are usually presented with a sample from which we wish to generalize a population. The standard deviation of a sample is denoted by s and is calculated by using the formula:

Where,

s = sample standard deviation

x= sample mean

   x = various observations

    n = number of observations in the sample

Example

Suppose you have the following set of numbers from a population: 12, 13, 14, 15, 16. Then the sample deviation is calculated as follows:
 

1. Calculate the sample mean of the data  =  (12 + 13 + 14 + 15 + 16) / 5 = 70 / 5 = 14
 

2. Subtract the mean from each data point and square this difference term.

(12 - 14)² = 4 ,  (13 - 14)² = 1 , (14 - 14)² = 0, (15 - 14)² = 1, (16 - 14)² = 4
 

3. Sum the squared differences and divide the total by n-1:

 (4 + 1 + 0 + 1 + 4)/ 4 = 10/4 = 2.5
 

4. The sample standard deviation is the square root of the term calculated in step 3: 2.5 = 1.581