An alternative measure of spread is the mean absolute deviation (MAD). It's almost the same as variance, but instead of squaring the differences, you take their absolute value. This has many advantages over variance:
1. You're now actually finding the average distance from the mean.
2. Variance can overweight extreme values due to the squaring.
3. The units of MAD are the same as the original quantity, rather than quantity squared.
4. MAD is more intuitive for non-statisticians. What does it actually mean for a sample to have a variance of 1 024 000 000 pounds squared?
Isn't it time statistics adopted MAD as the default measure of spread, rather than the outdated variance?