Informational
How to calculate standard deviation
Find the mean, subtract it from each value, square the differences, average those squares (divide by n − 1 for a sample, n for a population), then take the square root. Variance is the quantity before the square root.
What standard deviation measures
Standard deviation is a typical distance from the mean. A class where everyone scores near 80 has a small SD. A class spread from 40 to 100 has a large one. You need it for z-scores, t-tests, and many confidence intervals.
The two formulas
Use the sample formula unless the problem states you have every member of the population.
Step-by-step with a short list
Data: 2, 4, 4, 4, 5, 5, 7, 9. n = 8. Mean x̄ = 40/8 = 5.
- Deviations: −3, −1, −1, −1, 0, 0, 2, 4.
- Squares: 9, 1, 1, 1, 0, 0, 4, 16. Sum = 32.
- Sample variance s² = 32 / 7 ≈ 4.571.
- Sample SD s ≈ 2.14.
If you divided by 8 instead of 7 you would get σ ≈ 2.00 — a different answer to a different question.
Useful tips
- Keep extra decimal places until the last square root. Rounding the variance too early moves s.
- SD cannot be negative. If it is, a sign error happened in the squares.
- After you can compute s, z-scores are (x − mean) / SD.
Common mistakes
- Dividing by n on a sample homework set.
- Forgetting to square, then taking the square root of a sum of signed deviations (that sum is 0).
- Reporting variance when the question asked for standard deviation, or the reverse.
How Statistics Problem Solver Pro helps
The Standard Deviation & Variance calculator is listed as free and offline. Enter the dataset and compare s and σ. If the homework is a word problem rather than a list, scan it for the full steps. You can also look up the formula in the in-app reference.
Check s and σ on iPhone
The SD calculator stays free — no subscription.
Related guides
FAQ
Is variance the same as standard deviation?
No. Variance is SD squared (s² or σ²). SD is in the same units as the data; variance is in squared units.
See both formulas on the cheat sheet →Can I calculate standard deviation on iPhone offline?
Yes, with the built-in calculator in Statistics Problem Solver Pro. The listing says it works fully offline.
See all offline calculators →