# Root Mean Square Formula

Root mean square is also known as quadratic mean. Used in both, statistics and mathematics, this formula gives the total sum of square root of each data in an observation. It is generally denoted by $X_{rms}$.

The formula of root mean square is:

$\large X_{rms}=\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}….x_{n}^{2}}{n}}$

Where,
$x_{1},\; x_{2},\; x_{3}$ are observations
n is the total number of observations

#### Solved example

Question: Calculate the root mean square of the following observations; 5, 4, 8, 1 ?

Solution:

Using the Root Menu Square formula: $X_{rms}=\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}….x_{n}^{2}}{n}}$

$Root\;Mean\;Square=\sqrt{\frac{5^{2}+4^{2}+8^{2}+1^{2}}{4}}$

Root mean square = 5.14

#### Practise This Question

If  [aij]is an element of matrix A then it lies in ith row and jth column of the matrix