Mathematics
The Normal Distribution and the Empirical Rule for Data
Quick fact
In a perfect normal distribution, about 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three—so a value more than three standard deviations away is extremely rare, occurring less than 0.3% of the time.
Why this is interesting
Have you ever noticed that so many measurements—like heights or test scores—tend to cluster around an average, forming a bell-shaped curve? Why do these patterns appear so often, and can we use that shape to make predictions?