Question

Why do we square the variance and sq. Root for deviation?

Answer 1

Answer:

Step-by-step explanation:

Taking the square root gives you absolute homogeneity aka absolute scalability. For any scalar α and random variable X, we have:

Stdev[αX]=|α|Stdev[X]

Absolute homogeneity is a required property of a norm. The standard deviation can be interpreted as a norm (on the vector space of mean zero random variables) in a similar way that x2+y2+z2−−−−−−−−−−√ is the standard Euclidian norm in a three-dimensional space. The standard deviation is a measure of distance between a random variable and its mean.

Hope it helps you...