Absolute standard deviation vs relative standard deviation
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Consider three set of data having same mean and MD but their ranges are changing. It is interesting to see how SD changes with change in the range of the data. Show SET 1: 1, 3,5,7,9,11,13,15,17,19 Range:1-19 Mean=10, MD=5 SD= 6.05 SET 2: 2,3,5,7,7,9,13,15,14,23 Range: 1-23 Mean=10 MD=5 SD=6.28 SET 3: 3,5,5,7,7,8,10,12,13,30 Range: 1-30 Mean =10 MD=5 SD=7.70 It can be observed that all the three sets have same mean and MD. It is to be highlighted that while MD do not change with change in range, SD show changes with every change in ranges. This clearly establishes the supremacy of SD as compared to MD in dealing with variation in the data. 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. If the product comes lower, then the numbers are closer than its average. It is also knows as the coefficient of variation. The formula for the same is given as: \[\large RSD=\frac{s\times 100}{\overline{x}}\] Where, \(\begin{array}{l}\overline{x}\end{array} \) = Mean of the data. Solved ExamplesQuestion 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: \(\begin{array}{l}\overline{x}\end{array} \) = \(\begin{array}{l}\frac{\sum x}{n}\end{array} \) \(\begin{array}{l}\overline{x}\end{array} \) = \(\begin{array}{l}\frac{60+ 98+ 65+ 85}{4}=77\end{array} \) Calculation of standard deviation:
Formula for standard deviation: \(\begin{array}{l}s=\sqrt{\frac{\sum \left(x-\overline{x}^{2}\right)}{n-1}}\end{array} \)
\(\begin{array}{l}\sqrt{\frac{938}{3}}\end{array} \) S = 17.66 Relative standard deviation = \(\begin{array}{l}\frac{s\times 100}{\overline{x}}\end{array} \)
\(\begin{array}{l}\frac{17.66\times 100}{77}\end{array} \)
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. Disadvantages of Relative Standard Deviation: 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?
Hey 👋 I'm currently pursuing a Ph.D. in Maths. Prior to this, I completed my master's in Maths & bachelors in Statistics. I created this website for explaining maths and statistics concepts in the simplest possible manner. If you've found value from reading my content, feel free to support me in even the smallest way you can. What is the difference between absolute and relative deviation?The easiest way to differentiate relative dispersion/absolute dispersion is to check whether your statistic involves units. Absolute measures always have units, while relative measures do not.
What is the difference between absolute and standard deviation?The Mean Absolute Deviation (MAD) and Standard Deviation (STD) are both ways to measure the dispersion in a set of data. The MAD describes what the expected deviation is whereas the STD is a bit more abstract.
What does absolute standard deviation mean?Absolute deviation: the distance between each value in the data set and that data set's mean or median.
What is meant by relative standard deviation?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.
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