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Root Mean Square Calculator
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This calculator helps to determine the root mean square of the given observations. It is an online statistical calculator used for easy calculation. The equation for root mean square is mentioned below:

$X_{rms}$=$\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+....+x_{n}^{2}}{n}}$

Where $X_{rms}$ is the root mean square
x1,x2,..... are the given observations
n is the total number of observations

## Steps for Root Mean Square Calculator

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Step 1 :

Note down the given data from the question.

Step 2 :

Using the below mentioned equation, find out the root mean square value.

$X_{rms}$=$\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+....+x_{n}^{2}}{n}}$

## Problem on Root Mean Square Calculator

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1. ### Find out the root mean square value of the given data3,4,7,6?

Step 1 :

The observation is,

3,4,7,6

Step 2 :

Root mean square equation is,

$X_{rms}$=$\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+....+x_{n}^{2}}{n}}$

$X_{rms}$=$\sqrt{\frac{3^{2}+4^{2}+7^{2}+6^{2}}{4}}$

$X_{rms}$=$\sqrt{\frac{9+16+49+36}{4}}$

$X_{rms}$=$\sqrt{\frac{108}{4}}$=27

Answer  :

Root mean square, $X_{rms}$=27

2. ### Determine the root mean square value of 12,15,17.

Step 1 :

The given observations are,

12,15,17

Step 2 :

$X_{rms}$=$\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+....+x_{n}^{2}}{n}}$

$X_{rms}$=$\sqrt{\frac{12^{2}+15^{2}+17^{2}}{3}}$

$X_{rms}$=$\sqrt{\frac{144+225+289}{3}}$

$X_{rms}$=$\sqrt{\frac{658}{3}}$=219.3333

Answer  :

The answer is,

$X_{rms}$=219.3333

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