Part 1: Questions and Answers
Chapter 3
Q: How should we think about the meaning or interpretation of standard deviation?
A: As we say, the standard deviation (SD) captures the typical difference between a randomly chosen observation and the mean. It is not exactly the average but similar - so in our mind we may think as what kind of difference to expect. (The acerage would be simply the average absoulte difference, while here we have the square root of squared difference - often referred to as standardization.)
SD is useful to compare two distributions with the same mean. The one with higher SD will have more dispersion - ie we shall see observations more frequently / more farther from the mean. Indeed, in Finance, SD is a key measure of volaitility of asset prices, where high volatility implies more jumps in the price, and low volatility implies stability.
Importantly it has the same unit as our variable. For prices, both the mean and the standard deviation would be in currency units (ie dollars, euros, yen, etc)