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.

x	x-x	x-x²
45	-10.4	108.16
50	-5.4	29.16
55	-0.4	0.16
60	4.6	21.16
67	11.6	134.56

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

Related Calculator:

Percent Relative Standard Deviation