I understand from my lecturer that variance an standard deviation are central to statistics.
I do not understand the signifigance of both values, except that both measures the variability, and variance is the square of standard deviation. Why is there a need for two standards then?
Why must sd be squared to obtain variance? Why can't it be sd cubed, or even sd square rooted? Wouldnt sd cubed give us a more esaggerated value, which is better?
Also, how were these standards invented? They seem so non intuitive to me, then just takig a value then taking the difference wrt to the mean