The analysis behind this post began as research to look at the distribution of stock market returns on a daily, monthly and annual basis to see to what extent the distribution can be labeled a "normal distribution." The data that I analyzed, going back to 1900 on the Dow Jones shows that on a daily and monthly basis, the data-set follows some sort of bell curve, but on an annual basis return buckets are all over the map.
Sample size: 111
Average: 5.73% (not compounded and not including dividends)
Standard Deviation: 24.85%
Based on the way that I've bucketed annual returns, they don't appear to be clustered in any sort of bell curve. Returns were negative 38% of the time and greater than 20% almost 1/4 of the time.
Sample Size: ~28,000
Standard Deviation: 1.143%
Empirically, the Dow fluctuated between a 2% loss and 2% gain 94% of the time on a daily basis. The daily return of the Dow was between -0.7% and +0.7% 64% of the time.
Sample size: ~1300
Standard Deviation: 5.33%
Empirically, 77% of monthly returns are between 5% and -5%. 91% occur between -8% and 8%.