Standard Deviation Calculator
Standard deviation measures the spread of data around the mean: for the sample 2, 4, 4, 4, 5, 5, 7, 9 the sample standard deviation is 2.1380899 (the population value is 2).
Paste a column from Excel or type numbers separated by commas or spaces.
2.1380899352994
Full answer, then cut to fewer decimals (not rounded):
- 2.1380899352994
- 2.138089935299
- 2.13808993529
- 2.1380899352
- 2.138089935
- 2.13808993
- 2.1380899
- 2.138089
- 2.13808
- 2.1380
- 2.138
- 2.13
- 2.1
- Count n
- 8
- Mean x̄
- 5
- Median
- 4.5
- Variance s²
- 4.5714286
- Mean absolute deviation
- 1.5
- Range
- 7
- Coefficient of variation
- 42.7618 %
- Sum
- 40
Step-by-step solution
- Mean x̄ = Σx ÷ n = 40 ÷ 8 = 5
- Sum of squared deviations Σ(x − x̄)² = 32
- Variance s² = 32 ÷ (n − 1) = 32 ÷ 7 = 4.5714286
- s = √4.5714286 = 2.1380899
Standard Deviation Formula
s = √[Σ(x − x̄)² ÷ (n − 1)]
x̄ mean, n number of values; use N instead of n − 1 for a whole population
Worked Example
The sample 2, 4, 4, 4, 5, 5, 7, 9:
- Mean x̄ = Σx ÷ n = 40 ÷ 8 = 5
- Sum of squared deviations Σ(x − x̄)² = 32
- Variance s² = 32 ÷ (n − 1) = 32 ÷ 7 = 4.5714286
- s = √4.5714286 = 2.1380899
Mean x̄: 5 · Median: 4.5 · Variance s²: 4.5714286 · Mean absolute deviation: 1.5 · Range: 7 · Coefficient of variation: 42.7618 % · Sum: 40
Frequently asked questions
When do I use n − 1 instead of N?
Use n − 1 (sample) when the data are a sample used to estimate a larger population; it corrects the bias of dividing by n. Use N only when you have every member of the population.
What is the difference between variance and standard deviation?
Variance is the average squared deviation; standard deviation is its square root, in the same units as the data.
How do I calculate standard deviation in Excel?
=STDEV.S(range) for a sample and =STDEV.P(range) for a population. In R, sd(x) gives the sample value.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Standard Deviation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/standard-deviation-calculator/
IEEE
Scientific Converters, "Standard Deviation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/standard-deviation-calculator/