# Why was standard deviation invented?

As far as i know both variance and standard deviation is used for determining avarage deviating from the mean for each value in data set. So , if we can calculate it by using variance , why did we need to take square root of it to invent standard deviation ?

• The SD is on the same scale as the original variable. This makes it a lot easier to interpret it Jan 7, 2022 at 18:51
• A specific detail is that in a normal distribution the inflexions of the density function are 1 SD away from the mean. This shouldn't be thought a major rationale as variance and SD arise quite naturally in problems with quite different distributions such binomial, Poisson and exponential. The SD also has a general geometric interpretation (think Pythagoras' theorem in a suitable space). (Spotting which textbooks don't show this correctly on diagrams of normal distributions is a good diagnostic of books to be avoided.) Jan 7, 2022 at 19:02
• @NickCox can you give the name of a textbook which teaches these concepts clearly Jan 7, 2022 at 19:12
• See stats.stackexchange.com/questions/48347 for some suggestions.
– whuber
Jan 7, 2022 at 19:36
• I agree with the recommendation of Freedman, Pisani and Purves by @whuber in the thread he links to. Jan 7, 2022 at 23:26