Status Updates From Statistics: A complete intr...

Thatcher: “Everyone in the nation has benefited from the increased prosperity.” Says her comment shows a common error, that averages “provide information about the *spread* of values”. Avg inflation adjusted earnings rose 30% in the 80s, but inequalities resulted in debt and poverty. Cites figures showing inter-quartile spread went up 20%, but every decile income at more than doubled. What am I missing?

Why is a standard deviation determined by taking the square root of the sum of the squared deviations divided by the number in the batch? I get the math, but *why* does that result define the standard deviation?