Quadratic Mean

Quadratic mean :

Quadratic mean or also called root mean square (RMS), it's a type of mean like harmonic or geometric mean that we've already seen in previous articles.

The quadratic mean (rms) of a set of numbers is the square root of the sum of the squares of the numbers divided by the number of terms.

RMS is important in many branches of physics, chemistry and engineering, example; When you throw a ball it goes up in the air, slowing as it travels, then comes down again faster with the quadratic mean you can have an idea about the speed.

Formula :

• RMS = root mean square
• n = number of observations
• Xi = elements values
• The formula exists in discrete and continuous. In the continuous case it is the same formula except that instead of Xi it is Ci (center of value)
• We can also calculate a weighted quadratic mean by the formula:

Application :

Find the Root Mean Square of X, where X = [2, 3, 4, 7, 8]

• The number of elements (n) is 5
• Square all of the numbers X1 = [22, 32, 42, 72, 82]
• Add them up ; 4+9+16+49+64 =142
• Divide the sum on the number of elements n 142/5 =28.4
• Root of the result √?28.4
• RMS = 5.33

Weighted quadric mean (discrete?):

• RMS = √?(1220/200)
• RMS = 2.47

Weighted root mean square (continuous):

• Here we will take the central value of Xi, for the first row it is ( 0+5)/2
• RMS = √?(31375/300)
• RMS = 10.23

Example in Python

import numpy as np


X = [2,3,4,7,8]


squared_X = [x ** 2 for x in X]
squared_X


sum_squared = np.sum(squared_X)
sum_squared


a = sum_squared/len(X)
a


rms = np.sqrt(a)
rms