Cherry Picking The Diamonds From The Stock Market

How would I figure out this statistical question on stock indexes?


How would I figure this out:
What is the average amount by which a stock index moves in a one-month period? (e.g. SPY, QQQQ, etc.)
What is the amount of 1,2,3 standard deviations?
I think I’d need historical price data and a statistics program. What would be a good source for a table of historical stock index data?
Any hints on how to start?

Here are SPY and QQQQ monthly prices. You can find the rest by yourself at the below website.