Relative Standard Deviation Calculator

How to Calculate Relative Standard Deviation

Relative Standard Deviation (RSD), also known as the Coefficient of Variation (CV), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage and is defined as the ratio of the standard deviation to the mean.

Formula and Its Meaning

The formula for Relative Standard Deviation is:

\[RSD = \frac{s}{\bar{x}} \times 100\%\]

Where:

• \(s\) is the standard deviation of the sample
• \(\bar{x}\) is the mean of the sample

Calculation Steps

1. Calculate the mean of the dataset.
2. Calculate the standard deviation of the dataset.
3. Divide the standard deviation by the mean.
4. Multiply the result by 100 to express it as a percentage.

Example

Let's calculate the RSD for the dataset: 2, 4, 4, 4, 5, 5, 7, 9

1. Calculate the mean:
   \(\bar{x} = \frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = 5\)
2. Calculate the standard deviation:
   \(s = \sqrt{\frac{(2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2}{8}} \approx 2.14\)
3. Calculate the RSD:
   \(RSD = \frac{2.14}{5} \times 100\% \approx 42.8\%\)

Visual Representation

This diagram illustrates the RSD of our example dataset. The circle represents the relative spread of the data around the mean, with its radius proportional to the RSD percentage.