# What You Must Know (But Don't) About Relative Standard Deviation

There are many statistical concepts that come in handy, when handling large data sets. In this article, the calculation technique for relative standard deviation is presented in brief.

Omkar Phatak

Last Updated: Jun 3, 2018

Calculation Technique

Let me briefly explain how to calculate the mean and standard deviation for any data set.

The mean of any data set is obtained by summing up all its readings and dividing by their total number. For an array of data points X, with values ranging from x

Mean for the Array X = X

The mean of any data set is obtained by summing up all its readings and dividing by their total number. For an array of data points X, with values ranging from x

_{1}, x_{2}, ... x_{N}, the mean will be:Mean for the Array X = X

_{Mean}= (Σ_{n=1}^{N}x_{n})/NStandard Deviation (σ) = √[{Σ

_{n=1}

^{N}(x

_{n}- X

_{Mean})

^{2}}/{N - 1}]

*Relative standard deviation is the ratio of standard deviation of a data set, to its mean, which is then multiplied by 100.*It is used to compare the error in different data sets, with different mean values. As the units of mean and standard deviation are same, this ratio is a pure number, with no associated units.

Equation

This ratio is also known as percent standard deviation, as after all, it is a percentage. Here is the formula used for calculation.

*Relative Standard Deviation (RSD) = (Standard Deviation of a Data Set/Mean of a Data Set) x 100*Calculation Procedure

Here is the procedure:

- First calculate the mean of the data set, by summing up all values and dividing it by their total quantity.
- Once you get the mean, the next part is to calculate standard deviation.

- To do so, subtract all the data readings from the mean value, square the difference for each value and calculate the sum of the squares for all values.
- Then, using the formula listed above, calculate it.
- Divide the standard deviation by the mean of the data set and multiply it by 100, to get the percent relative standard deviation.