Here is the formula for the variance : $\sigma^2=\dfrac{\sum(X-\mu)^2}{N}$.

My question is why do we SQUARE the difference between the mean and the variable, why don't we use absolute value ...The result will be different!

I saw online that it's to make the value positive, but like why don't we choose 4 or 6 as exponent? 

Hope someone can enlighten me! 

Thanks :)
Ayman