And it is easier to use algebra on squares and square roots than absolute values, which makes the standard deviation easy to use in other areas of mathematics. But I get your point and have taken "natural parameters" out of my answer.
Here, these numbers are further away from 10. I mean, the furthest number here is two away from 10.
So the variance of this less-dispersed data set is a lot smaller. Measures of dispersion quartiles, percentiles, ranges provide information on the spread of the data around the centre.
There you go. The SD is usually more useful to describe the variability of the data while the variance is usually much more useful mathematically.
The standard deviation has proven to be an extremely useful measure of spread in part because it is mathematically tractable. Which city has the more consistently priced petrol?
From that, I'm going to subtract our mean and I'm going to square that. Jan 27 '16 at 19: This wouldn't be true of the SD. More precisely, it is a measure of the average distance between the values of the data in the set and the mean. Why square the differences?
I know that sounds very complicated, but when I actually calculate it, you're going to see it's not too bad. Thank you for your interest in this question.
It's easy to prove to yourself that the two equations are equivalent. Standard Deviation and Variance 1 of 2 The variance and the closely-related standard deviation are measures of how spread out a distribution is. So what people like to do is talk in terms of standard deviation, which is just the square root of the variance, or the square root of sigma squared.