The square root of the mean of the squares of a set of values.

Steps:

• square each value

• add them

• divide by how many values there are (= the arithmetic mean)

• take the square root of that

Example: The Root Mean Square of 5, 7 and 11 is:

√( [5^{2}+7^{2}+11^{2}]/3 )

= √( [25+49+121]/3 )

= √( 195/3 )

= √( 65 )

= 8.062...

Definition of