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Relative Standard Deviation Calculator
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Standard Deviation is used to the measure the variability in the data for the given set of data. The Relative standard deviation is the measurement of the coefficient of variation expressed in percentage. In order to measure the precision of the given data, we use the relative standard deviation.
Relative Standard Deviation Calculator calculates the Mean, variance, standard deviation and relative standard deviation (RSD) for a given set of data.

 

Steps for Relative Standard Deviation Calculator

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Step 1 :  

Read the problem. Note down the no of items given as N. Find the Arithematic mean of the given data using the formula:


$\bar{x}$ = $\frac{\sum{x}}{N}$


where $\sum{x}$ = sum of the given data
N = no of data given.



Step 2 :  

Calculate the deviation of each item among the given data with the mean. Also square the deviation to get (x - \bar{x})2. Calculate $\sum(x - \bar{x})^{2}$.



Step 3 :  

To calculate the Variance $\sigma$ use the formula:


$\sigma$ = $\frac{\sum(x - \bar{x})^{2}}{N-1}$


where N is the no of items given. Take the Square root of variance to get the standard deviation (S).



Step 4 :  

To get the Relative standard deviation, divide the Standard deviation with the mean given by formula:


RSD = $\frac{S}{\bar{x}}$ $\times$ 100%.



Problems on Relative Standard Deviation Calculator

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  1. Find the Relative standard deviation for the given data: 3, 6, 9, 12, 15, 18.


    Step 1 :  

    Given data are:3, 6, 9, 12, 15, 18.


    no of items given N = 6.


    To find Mean of the numbers:

    $\bar{x}$ = $\frac{3 + 6 + 9 + 12 + 15 + 18}{6}$ = 10.5



    Step 2 :  
    x(x - $\bar{x}$)(x - $\bar{x}$)2
    37.556.25
    64.520.25
    91.52.25
    121.52.25
    154.520.25
    187.556.25

     



    Step 3 :  

    The Variance $\sigma$ = $\frac{\sum(x - \bar{x})^{2}}{N-1}$


    $\sigma$ = $\frac{157.5}{6-1}$


                    = 31.5.


    The standard deviation S = $\sqrt{\frac {\sum(x - \bar{x})^{2}}{N-1}}$


     S = $\sqrt{31.5}$


        = 5.61248.



    Step 4 :  

    Relative Standard deviationis given by


    RSD = $\frac{S}{\bar{x}}$ $\times$ 100%


    RSD = $\frac{5.61248}{10.5}$ $\times$ 100 %


    = 53.45 %.



    Answer  :  

    Hence we get Mean = 10.5, Variance = 31.5, Standard deviation = 5.61248 and RSD = 53.45%.
    The Relative standard deviation RSD = 53.45 %.



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