Standard Deviation Calculator — Variance, Mean & Coefficient of
Compute standard deviation, variance, mean, median, range, and coefficient of variation from any dataset. Free online calculator with step-by-step results.
Standard Deviation
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Mean (Average)
17.125
Variance
12.125
Median
17
Count (n)
8
Range
12 to 22 (span: 10)
Coefficient of Variation
20.33%
Scenario Comparison
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Data Distribution with Standard Deviation
Data Set (sorted)
Step 1: Calculate the Mean (x̄)
x̄ = (12 + 15 + 18 + 22 + 14 + 19 + 16 + 21) ÷ 8= 17.125
Step 2: Deviations & Squared Deviations
Table of (xᵢ − x̄) and (xᵢ − x̄)²
| i | xᵢ | xᵢ − x̄ | (xᵢ − x̄)² |
|---|---|---|---|
| 1 | 12 | -5.125 | 26.265625 |
| 2 | 15 | -2.125 | 4.515625 |
| 3 | 18 | 0.875 | 0.765625 |
| 4 | 22 | 4.875 | 23.765625 |
| 5 | 14 | -3.125 | 9.765625 |
| 6 | 19 | 1.875 | 3.515625 |
| 7 | 16 | -1.125 | 1.265625 |
| 8 | 21 | 3.875 | 15.015625 |
| Sum | 0 | 84.875 | |
Step 3: Variance
σ² = 84.875 ÷ (n − 1) = 84.875 ÷ 7 = 12.125
Step 4: Standard Deviation
σ (or s) = √(12.125) = 3.482097
Mean
17.125
Median
17
Min / Max
12 / 22
CV
20.33%
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