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# Relative Standard Deviation Formula

Standard Deviation is the measurement of deviation of various terms from their average in an observation. It tells how the different numbers in a data are scattered around the mean, while relative standard deviation is measured in percentage. It is also called percent relative standard deviation. It reflects spread of the data in percent.

A higher relative standard deviation means that the numbers are widely spread from its average, while a lower relative standard deviation means the numbers are more closer to its average. Relative standard deviation is often termed as coefficient of variation. It is the absolute value of coefficient of variation. The abbreviation used for relative standard deviation is RSD or %RSD. Formula for relative standard deviation is given below:
Where,
RSD = Relative standard deviation
S = Standard deviation
$\bar{x}$ = Mean of the data.

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## Relative Standard Deviation Problems

Few problems based on relative standard deviation are given below :

### Solved Examples

Question 1: Following are the marks obtained in by 4 students in mathematics examination: 75, 98, 65, 80. Calculate the relative standard deviation ?

Solution:

Formula of the mean is given by:
$\bar{x}$ = $\frac{\sum x}{n}$

$\bar{x}$ = $\frac{75+98+65+80}{4}$ = 79.5 $\$$Calculation of standard deviation:  x$x-\bar{x}(x-\bar{x})^{2}$75 -4.5 20.25 98 18.5 342.25 65 -14.5 210.25 80 0.5 0.25$\sum (x-\bar{x})^{2}$= 573 Formula for standard deviation: S =$\sqrt{\frac{\sum (x-\bar{x})^{2}}{n-1}}$S =$\sqrt{\frac{573}{3}}$S = 13.82 Relative standard deviation =$\frac{S*100}{\bar{x}}$=$\frac{13.82*100}{79.5}$= 17.38% Question 2: During a survey, the differences between maximum and minimum temperature are recorded. Following are the five consecutive values: 6, 10, 12, 8, 9. Find the relative standard deviation ? Solution: Formula for mean:$\bar{x}$=$\frac{\sum x}{n}\bar{x}$=$\frac{6+10+12+8+9}{5}\bar{x}$= 9 Calculation for standard deviation  x$x-\bar{x}(x-\bar{x})^{2}$6 -3 9 10 1 1 12 3 9 8 -1 1 9 0 0$\sum (x-\bar{x})^{2}$= 20 Formula for standard deviation: S =$\sqrt{\frac{\sum (x-\bar{x})^{2}}{n-1}}$S =$\sqrt{\frac{20}{4}}$= 2.236 Relative standard deviation =$\frac{S*100}{\bar{x}}$=$\frac{2.236*100}{9}\$

= 24.85%

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