the 68-95-99.7 rule
If a dataset is bell-shaped, how much of it lands close to the average, and how much strays far out? The 68-95-99.7 rule is the handy rule of thumb that answers this for any normal distribution, letting you read off probabilities in your head without a table.
For X ~ Normal(mu, sigma), measure distance from the mean in standard deviations. About 68% of the values fall within one sigma of the mean (between mu - sigma and mu + sigma); about 95% fall within two sigma; and about 99.7% fall within three sigma. The complements are just as useful: roughly 32% lie beyond one sigma, about 5% beyond two sigma (so a '2-sigma event' is around a 1-in-20 occurrence), and only about 0.3% beyond three sigma (about 1 in 370). These three numbers are simply the areas under the bell curve over those central bands.
This rule turns the abstract standard deviation into something tangible: sigma is the natural unit of 'usual variation', and being more than two or three sigma from the mean is a quick flag for 'unusually large'. It underlies quality-control limits and the common '2-sigma significance' shorthand. The crucial caveat is in its old name, the empirical rule: it holds only for roughly normal data. For skewed or heavy-tailed distributions these percentages are simply wrong — Chebyshev's inequality gives weaker bounds that hold for any distribution.
IQ scores are scaled to Normal(mu = 100, sigma = 15). So about 68% of people score between 85 and 115, about 95% between 70 and 130, and only about 0.3% score above 145 or below 55.
One, two, three sigma capture about 68%, 95%, and 99.7% of a bell curve.
These percentages are specific to the NORMAL distribution; applying 68-95-99.7 to skewed or heavy-tailed data will badly understate how often extreme values occur.