Relative Standard Deviation

One of the most important parts of any experiment is the mathematical analysis of results. A branch of mathematics which is completely devoted to the study of data and its analysis is of course statistics. There are several statistical constructs, which are regularly employed when analyzing experimental data.

What is Relative Standard Deviation?

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 the readings of a data set and dividing by their total number. For an array of data points X, with points ranging from x₁, x₂, ... x_N, the mean will be:

Mean for the Array X = X_Mean = (Σ_n=1^N x_n)/N

The standard deviation or of a data set, gives you an idea about how precise the experimental results are and how much they deviate from the mean. A high standard deviation value points towards a highly imprecise set of results, while a low standard deviation value, indicates that the results are more precise and closer to the mean value. Here is the formula for standard deviation (denoted by σ):

σ = √[{Σ_n=1^N (x_n - X_Mean)²}/{N - 1}]

The above formula is not as complicated as it looks. Standard deviation is a precise measurement of random errors caused in an experiment.

Relative standard deviation is a ratio of standard deviation of a data set, to its mean, which is then multiplied by 100. As the units of mean and standard deviation are same, this ratio is a pure number, with no associated units. While standard deviation helps you understand the error level in one data set, relative standard deviation is used to compared the error in different data sets, with different mean values. Let us take a look at the equation of standard deviation in the following lines.

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

It is possible to calculate this ratio using Excel, by listing all the data neatly in columns and using formula function. Here is the calculation procedure:

• First calculate the mean of the data set, by summing up all values and dividing it by their total number.
• Once you get the mean, the next part is to calculate standard deviation.
• To calculate standard deviation, 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 standard deviation.
• Divide the standard deviation by the mean of the data set and multiply it by 100, to get the percent relative standard deviation.

The calculation itself is not complicated but tedious. Knowing how to find standard deviation will be helpful. You need to work out the standard deviation value accurately in order to be able to calculate percent relative standard deviation precisely. If you are a student of chemistry or physics, you are bound to employ this calculation method when analyzing experimental data, generated in the lab.