# 12. Standard Deviation¶

The expected value $$\mu_X$$ of a random variable $$X$$ is a measure of the center of the distribution of $$X$$. But we know that $$X$$ need not be equal to $$\mu_X$$; indeed, $$\mu_X$$ need not even be a possible value of $$X$$.

How far from $$\mu_X$$ can $$X$$ be? This chapter develops an answer to that question, by examining the mean squared error familiar to you from Data 8.