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# Calculate Relative Standard Deviation - Definition, Formula, Example

## How to Calculate Relative Standard Deviation (RSD) - Tutorial

##### Definition:

This tutorial explains how to calculate the value of Relative Standard Deviation.

#### Formula:

S = √(Σ(x-x)2/N-1) RSD =S*100/ x
###### Where,
Mean = X/N X - Summation of x value N = The count of mean values S = Standard Deviation value x = Mean of the data
##### Example :

The Weight of a group of 5 persons are 45,50,55,60,67. Calculate the standard deviation of those persons.

##### Given :

Mean Values (X) = 45,50,55,60,67 N = 5

##### To Find :

Relative standard deviation (RSD)

##### Solution :
###### Step 1:

Let us first calculate the value of x,

 x = (45+50+55+60+67)/ 5 = 277/5 = 55.4
###### Step 2:

Calculate the value of x, x-x, x-x2.

xx-xx-x2
45-10.4108.16
50-5.429.16
55-0.40.16
604.621.16
6711.6134.56
###### Step 3:

Now, let us calculate the value of Standard Deviation(S).

S =√(Σ(x-x)2/N-1)

S =√(293.20000000000005)/4   = 8.56

###### Step 4:

Relative Standard Deviation Calculation:

RSD = S*100 / x

=(8.56*100)/55.4         = 15.45

##### Result :

Standard Deviation = 8.56 Relative Standard Deviation = 15.45