# What do the mean deviation, variance and standard deviation all have in common? How is this common factor (s) helpful with the calculations of the mean deviation, variance and standard deviation?

What do the mean deviation, variance and standard deviation all have in common? How is this common factor (s) helpful with the calculations of the mean deviation, variance and standard deviation?
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Isma Jimenez
Mean deviation, standard deviation and variance all measure the spread of the distribution. Mean deviaiton is the average of absolute difference of all data points fro its mean. Standard deviation also tell us about the data points in any distribution are spread around its mean. Variance also tell us about the spread of the distribution and it is the average of square the difference of data points from the mean.
So in all the three measure of spread the common factor is the differnece of data points from mean and the total number of data points.
The mean deviation, standard deviation and variance of data distribution ${X}_{1},{X}_{2},\dots .,{X}_{n}$ are calculated using the below mentioned formulae
So here mean and the sample size are common factors in calculation of measures of spread and are calculated as shown below.
Mean devaition $=\frac{\sum _{i=1}^{n}|{X}_{I}-\stackrel{―}{X}|}{n}$
Standard deviation $=\sqrt{\frac{\sum _{i=1}^{n}|{X}_{I}-\stackrel{―}{X}|}{n-1}}$
Variance $=\sum _{i=1}^{n}\frac{{\left({X}_{I}-\stackrel{―}{X}\right)}^{2}}{n-1}$
where $\stackrel{―}{X}=\frac{\sum _{i=1}^{n}{X}_{I}}{n}$ and n is sample size