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

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