Root Mean Square
What is Root Mean Square (RMS)?
Statistically, the root mean square (RMS) is the square root of the mean square, which is the arithmetic mean of the squares of a group of values. RMS is also called a quadratic mean and is a special case of the generalized mean whose exponent is 2. Root mean square is also defined as a varying function based on an integral of the squares of the values which are instantaneous in a cycle.
In other words, the RMS of a group of numbers is the square of the arithmetic mean or the function’s square which defines the continuous waveform.
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Root Mean Square Formula
The formula for Root Mean Square is given below to get the RMS value of a set of data values.
For a group of n values involving {x_{1}, x_{2}, x_{3},…. X_{n}}, the RMS is given by:
- x_{rms :}\(\sqrt{{\frac{(x_{1}^{2}+x_{2}^{2}…x_{n}^{2})}{N}}}\)
The formula for a continuous function f(t), defined for the interval T_{1} ≤ t ≤ T_{2} is given by:
- f_{rms} = \(\sqrt{\frac{1}{T_{2}-T_{1}}\int_{T_{1}}^{T_{2}}[f\left ( t \right )^{2}dt}]\)
The RMS of a periodic function is always equivalent to the RMS of a function’s single period. The continuous function’s RMS value can be considered approximately by taking the RMS of a sequence of evenly spaced entities. Also, the RMS value of different waveforms can also be calculated without calculus.
How to Calculate the Root Mean Square
Steps to Find the Root mean square for a given set of values are given below:
Step 1: Get the squares of all the values
Step 2: Calculate the average of the obtained squares
Step 3: Finally, take the square root of the average
Try out: Root Mean Square Calculator
Solved Example
Question:
Calculate the root mean square (RMS) of the data set: 1, 3, 5, 7, 9
Solution:
Given set of data values:
1, 3, 5, 7, 9
Step 1: Squares of these values
1^{2}, 3^{2}, 5^{2}, 7^{2}, 9^{2}
Or
1, 9, 25, 49, 81
Step 2: Average of the squares
(1 + 9 + 25 + 49 + 81)/5
= 165/5
= 33
Step 3: Take the square root of the average.
RMS = √33 = 5.745 (approx)
Root Mean Square Error (RMSE)
The Root Mean Square Error or RMSE is a frequently applied measure of the differences between numbers (population values and samples) which is predicted by an estimator or a mode. The RMSE describes the sample standard deviation of the differences between the predicted and observed values. Each of these differences is known as residuals when the calculations are done over the data sample that was used to estimate, and known as prediction errors when calculated out of sample. The RMSE aggregates the magnitudes of the errors in predicting different times into a single measure of predictive power.
Root Mean Square Error Formula
The RMSE of a predicted model with respect to the estimated variable x_{model} is defined as the square root of the mean squared error.
- RMSE =\(\sqrt{\frac{\sum_{i=1}^{n}(X_{obs,i}-X_{model,i})^{2}}{n}}\)
Where, x_{obs} is observed values, x_{model} is modelled values at time i.
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Frequently Asked Questions – FAQs
What is the root mean square?
How is RMS calculated?
What is the RMSE value?
Is a higher or lower RMSE better?
What is the value of RMS for the data set 2, 3, 5, 7, 11?
RMS = square root(41.6) or √41.6 = 6.45