Relative Standard Deviation Formula
Relative standard deviation is also called percentage relative standard deviation formula, is the deviation measurement that tells us how the different numbers in a particular data set are scattered around the mean. This formula shows the spread of data in percentage.
If the product comes to a higher relative standard deviation, that means the numbers are very widely spread from its mean.Â
If the product comes lower, then the numbers are closer than its average. Â It is also knows as the coefficient of variation.
The formula for the same is given as:
\[\large RSD=\frac{s\times 100}{\overline{x}}\]
RSD = Relative standard deviation
s = Standard deviation
Solved Examples
Question 1: Following are the marks obtained in by 4 students in mathematics examination: 60, 98, 65, 85. Calculate the relative standard deviation ?
Solution:
Formula of the mean is given by:
Calculation of standard deviation:
\(\begin{array}{l}x\end{array} \) |
\(\begin{array}{l}x-\overline{x}\end{array} \) |
\(\begin{array}{l}\left(x-\overline{x}\right)^{2}\end{array} \) |
| 60 | -17 | 289 |
| 98 | 21 | 441 |
| 65 | -12 | 144 |
| 85 | 8 | 64 |
\(\begin{array}{l}\sum \left(x-\overline{x}\right)^{2}=938\end{array} \) |
Formula for standard deviation:
S =
S =
S = 17.66
Relative standard deviation =
=
= 22.93%
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