Quadratic Mean Calculator

Enter a set of numbers to compute the quadratic mean.

Compute the Quadratic Mean of a Set of Numbers

Result

What Is the Quadratic Mean?

The quadratic mean, also known as the root mean square (RMS), is the square root of the arithmetic mean of the squares of a set of numbers. It is widely used to measure the magnitude of a dataset, particularly in applications involving distances or energy. The formula is: \( R = \sqrt{\frac{1}{n} \sum_{i=1}^{n} x_i^2} \) Where:

\( n \) is the total number of data points,
\( x_i \) represents each individual data point,
\(\sum\) denotes summation.

How to Calculate the Quadratic Mean?

Steps:

Square each data point and calculate the sum of the squared values.
Divide the sum of the squares by the number of data points to get the mean of the squares.
Take the square root of the mean to obtain the quadratic mean.

Examples

Example 1: Calculate the Quadratic Mean of 3, 4, and 5

Solution:

1. Calculate the Sum of the Squared Values:

\( 3^2 + 4^2 + 5^2 = 9 + 16 + 25 = 50 \)

2. Mean of the Squares:

\( \frac{50}{3} \approx 16.66666 \)

3. Quadratic Mean:

\( R = \sqrt{16.66666} \approx 4.08 \)

Example 2: Calculate the Quadratic Mean of 2, -2, and 6

Solution:

1. Calculate the Sum of the Squared Values:

\( 2^2 + (-2)^2 + 6^2 = 4 + 4 + 36 = 44 \)

2. Mean of the Squares:

\( \frac{44}{3} \approx 14.66666 \)

3. Quadratic Mean:

\( R = \sqrt{14.66666} \approx 3.83 \)