Mean, variance and standard deviation calculator
Paste your values, e.g. copied from a spreadsheet. You get mean, median, mode, range, variance and standard deviation, for a sample (n − 1) and for a population (n).
Result
- Count n
- 8
- Mean x̄
- 5
- Median
- 4.5
- Mode
- 4
- Range
- 7 (2 … 9)
- Sample variance s² (n − 1)
- 4.5714
- Sample standard deviation s
- 2.1381
- Population variance σ² (n)
- 4
- Population standard deviation σ (n)
- 2
- Coefficient of variation s / x̄
- 42.76%
Whether to divide by n or n − 1 depends on the task: n − 1 for a sample (estimate), n for a whole population.
Workings
- 1Sorted: 2; 4; 4; 4; 5; 5; 7; 9
- 2x̄ = sum / n = 40 / 8 = 5
- 3n is even: median = mean of positions 4 and 5 = (4 + 5) / 2 = 4.5
- 4Sum of squared deviations Σ(xᵢ − x̄)² = 32
- 5s² = 32 / (n − 1) = 32 / 7 = 4.5714; s = √s² = 2.1381
- 6σ² = 32 / n = 32 / 8 = 4; σ = 2
The formulas
- Mean: x̄ = Σxᵢ / n.
- Sample variance: s² = Σ(xᵢ − x̄)² / (n − 1).
- Population variance: σ² = Σ(xᵢ − x̄)² / n.
Frequently asked questions
How do I separate the values?+
With spaces, commas, semicolons or line breaks; use a point as the decimal mark.