Standard deviation

Standard deviation is a measure of how far the data goes from the mean in a given data set.
It can be calculated by the following procedure:

Let us take an example of the following data set:

2, 3, 5, 7, 11, 12  

Step 1: Calculate the mean of the given data.

Mean = Sum of data elements / number of elements in data set

Mean = (2 + 3 + 6 + 8 + 11 + 12) /  6

Mean =  42 / 6

Mean = 7

Step 2: Calculate the square of the distance of each element of the data set from the mean:

Distance squared = (Number - Mean)^2

• Distance squared for first number = ( 2 - 7)^2 = 25
• Distance squared for second number = (3 - 7)^2 = 16
• Distance squared for third number = (5 - 7)^2 = 4
• Distance squared for fourth number = (7 - 7)^2 = 0
• Distance squared for fifth number = (11 - 7)^2 = 16
• Distance squared for sixth number = (12 - 7)^2 = 25

Step 3: Find the mean of each of the distance squared obtained above.

Mean of the distance squared obtained above = (25 + 16 + 4 + 0 + 16 + 25) / 6 

Mean of the distance squared obtained above = (83) / 6 = 13.83

Step 4: The square root of the value obtained above (mean) is the Standard Deviation of the given data set. Therefore we have:

Standard Deviation = square root of 13.83

Standard Deviation =  3.7