STANDARD DEVIATION FOR GROUPED DATA

Standard Deviation for Discrete Frequency Distribution

Mean Method :

Assumed Mean Method :

Let x₁, x₂, x₃, ...........x_n be the observations in the given data with frequencies f₁, f₂,f₃, .......fn respectively. Let x bar be their mean and A be the assumed mean.

Standard Deviation for Continuous Frequency Distribution

Mean Method :

where x_i = Middle value of the i^th class.

f_i = Frequency of the i^th class

Step Deviation Method : 

To make the calculation simple, we provide the following formula. Let A be the assumed mean, xi be the middle value of the i^th class and c is the width of the class interval.

Standard Deviation Calculator

Example 1 :

The rainfall recorded in various places of five districts in a week are given below.

Solution :

Σf  =  N  =  40

Σfd²  =  2450

(Σfd²/N)  =  (2450/40)  

Σfd  =  40

(Σfd/N)²  =  (40/40)²  =  1

σ  =  √(245/4) - 1

σ  =  √(245-4)/4

σ  =  √(241/4)

σ  =  √60.25

σ  =  7.76

Example 2 :

In a study about viral fever, the number of people affected in a town were noted as

Find its standard deviation.

Solution :

Σf  =  N  =  65

Σfd²  =  556

(Σfd²/N)  =  (556/65)   =  8.55

Σfd  =  6  =  Σfd/N  =  6/65  =  0.09

σ  =  √(8.55 - 0.09) ⋅ 5

σ  =  (√8.46) ⋅ 5

σ  =  (2.91) ⋅ 5

σ  =  14.55

The standard deviation is approximately 14.6. 

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