Standard Deviation Calculator
Enter numbers separated by commas to compute the standard deviation, variance, mean, sum and 95% margin of error. Toggle between population (÷n) and sample (÷n−1) treatment and see every deviation in the working table.
TheCalculators — Standard Deviation Calculator
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Standard deviation (σ)
4.898979
8 values · population ÷ n · variance 24
- Count (n)
- 8
- Sum (Σx)
- 144
- Mean (μ or x̄)
- 18
- Variance (σ²)
- 24
- Std dev (σ)
- 4.898979
- Sample variance (s²)
- 27.428571
- Sample std dev (s)
- 5.237229
- Population σ
- 4.898979
- Min
- 10
- Max
- 23
- Range
- 13
- 95% margin of error (1.96·σ/√n)
- ± 3.39482
Step-by-step solution
- 1Compute the meanx̄ = Σx/n = 144 / 8 = 18
- 2Sum of squared deviationsΣ(x − x̄)² = 192
- 3Divide by n (population)σ² = 192 / 8 = 24
- 4Take the square rootσ = √24 = 4.898979
Squared deviations
Sum of the last column ÷ (n or n−1) gives the variance.
Data values
Most useful next
Formula
σ = √(Σ(xᵢ − μ)²/N) · s = √(Σ(xᵢ − x̄)²/(n−1)) · ME₉₅ = 1.96·σ/√n
Pro tips
- • Sample vs population: if in doubt with collected data, you usually want the sample version (÷ n−1).
- • Standard deviation shares the units of the data; variance does not (units²).
- • Roughly 68% of normal data falls within ±1σ of the mean.
FAQ
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