2
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Well , s.d. can be cubed or squared to obtain " fractional order moments about mean " , though I have not seen such kind of a thing anywhere. $\endgroup$ – Souvik Dey Oct 19 '12 at 5:21
  • $\begingroup$ The variance has a number of nice properties, most importantly that the variance of a sum of independent random variavles is the sum of the variances. $\endgroup$ – André Nicolas Oct 19 '12 at 5:35
  • $\begingroup$ The nice thing about standard deviation, on the other hand, is that it scales like the random variable ($\sigma_{aX} = |a| \sigma_X$), so it has the same units as the random variable. $\endgroup$ – Robert Israel Oct 19 '12 at 5:55
2
$\begingroup$

Variance is one of the so called moments and plays a very important role in Statistics. To be more intuitive just imagine how would be a measure of variance if you just take the normalized sum of differences between all values around some central value: those differences who are negative will influence in a mistaken way your dispersion measurement.

There are many applications of these concepts. To cite one example: with standard variation, engineers can guarantee if 99% of all production of an industry will lay within a specified interval of tolerance.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.