What Standard Deviation Really Tells You About Your Data
September 18, 2026
For roughly normally distributed (bell-curve) data, about 68% of values fall within 1 standard deviation of the mean, about 95% fall within 2, and about 99.7% fall within 3 — known as the empirical rule, and it's what makes a standard deviation number actually meaningful rather than abstract.
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Open the Standard Deviation Calculator →The Empirical Rule (68-95-99.7)
| Range | % of data (normal distribution) |
|---|---|
| Mean ± 1 standard deviation | ~68% |
| Mean ± 2 standard deviations | ~95% |
| Mean ± 3 standard deviations | ~99.7% |
A Practical Example
Suppose a class's test scores have a mean of 75 and a standard deviation of 8. By the empirical rule: about 68% of students scored between 67 and 83, about 95% scored between 59 and 91, and only about 0.3% of students scored outside 51-99 in either direction.
When the Empirical Rule Doesn't Apply
The 68-95-99.7 percentages only hold for data that's roughly normally distributed (symmetric, bell-shaped). Skewed data — like income, wait times, or most real-world 'time until failure' data — doesn't follow these percentages, even though you can still calculate a standard deviation for it. Standard deviation is always calculable; the empirical rule's specific percentages are not always applicable.
Frequently Asked Questions
What percentage of data falls within 1 standard deviation of the mean?
About 68%, for data that's roughly normally (bell-curve) distributed.
What is a z-score?
A z-score is the number of standard deviations a value is from the mean, calculated as z = (x − mean) / standard deviation. A z-score of 2 means the value is 2 standard deviations above average.
Does standard deviation work for any data distribution?
You can calculate standard deviation for any numeric data set, but the empirical rule's specific percentages (68-95-99.7) only apply to data that's roughly normal/bell-shaped — skewed data won't follow those percentages even though it still has a valid standard deviation.
How is standard deviation used in quality control?
Manufacturing quality control (like Six Sigma) uses standard deviation to flag values outside an expected range — a measurement more than 3 standard deviations from the target is treated as a statistically rare defect worth investigating.
What's a coefficient of variation?
Coefficient of variation is standard deviation divided by the mean, expressed as a percentage — it lets you compare relative variability between two data sets that use different units or have very different average sizes.