Why do we need variance whereas we have standard deviation instead?
Why do we need variance whereas we have standard deviation instead? I know standard deviation comes from variance numerically. and gives more clarity about the deviation of data from a mean.
Thank you for your question!
You are correct, the variance can't really give us a true appreciation of the spread of the data (given in some units), as it has the dimension of squared units. We would need to take the square root of the variance to go back to the original units - that is how we obtain standard deviation.
Indeed, standard deviation is the more intuitive metric to work with. However, variance is a convenient mathematical notion. If you wish to dig deeper into the mathematics of it, the final pages of the course notes provide a thorough derivation.
Hope this helps!
I want to add that we need variance to calculate correctly the deviations from the mean, because they can be negative and positive: when you square -2 you get 4, when you square 2 you also get 4. In both cases the module of number (4) is the same, so the deviation from the mean value is the same. Standard deviation is the square root of the sum of all the deviations calculated this way and allows us to compare it with the original units.