# Relative Standard Deviation

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The relative standard deviation is the ratio of the standard deviation to the absolute value of the mean of the given data. The relative standard deviation (R.S.D) is a measure of the dispersion of the data, that is, it tells us how much the data is spread apart. The relative standard deviation tells us how much larger the standard deviation of our data is, as compared to the mean of the data.

The formula for relative standard deviation is given as,

Relative Standard Deviation R.S.D = σ/|µ| where,

µ is the mean of the data,

and, σ is the standard deviation of the data.

Relative Standard Deviation (R.S.D) vs Coefficient of Variation (C.V):

The relative standard deviation (R.S.D) is similar to the coefficient of variation of the data except for the fact that to calculate R.S.D we have to divide by the absolute value of the mean. Hence the relative standard deviation will always be positive irrespective of whether the mean is positive or negative.

Note that it is not possible to calculate relative standard deviation if the mean is equal to 0 as we cannot divide by 0. If the mean is very close to zero then the value of R.S.D will be very large and in such cases it is much better to calculate other measures of dispersion to know about the spread of the data

How to calculate relative standard deviation?

1. Calculate the mean of the data using the formula x̄ = ∑xi /n where xi denotes the sample values and n denotes the size of the sample.
2. Calculate the variance of the data using the formula, Variance=∑(xi– x̄)2/n
3. Take the square root of the variance to find the standard deviation.
4. Find the relative standard deviation using the formula, R.S.D = σ/|µ|. Notice that we divide by the absolute value of the mean.

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