Standard Deviation Calculator
Calculate standard deviation, variance, and related statistics
Calculate as:
Standard Deviation (Sample)
5.2372
s = √[Σ(x - x̄)² / 7]
Variance (Sample)
27.4286
s² = Σ(x - x̄)² / 7
Count (n)
8
Sum
144
Mean (x̄)
18
Σ(x - x̄)²
192
Population vs Sample
| Measure | Population (÷n) | Sample (÷(n-1)) |
|---|---|---|
| Variance (s²) | 24 | 27.4286 |
| Std Deviation (s) | 4.8990 | 5.2372 |
Use population when your data includes the entire population. Use sample when your data is a sample of a larger population (more common).
Calculation Steps
| Value (x) | Deviation (x - x̄) | (x - x̄)² |
|---|---|---|
| 10 | -8 | 64 |
| 12 | -6 | 36 |
| 23 | 5 | 25 |
| 23 | 5 | 25 |
| 16 | -2 | 4 |
| 23 | 5 | 25 |
| 21 | 3 | 9 |
| 16 | -2 | 4 |
| Sum | 0 | 192 |
Z-Scores
Z-score = (x - x̄) / s = how many standard deviations from the mean
10(-1.5275)
12(-1.1456)
23(+0.9547)
23(+0.9547)
16(-0.3819)
23(+0.9547)
21(+0.5728)
16(-0.3819)
|z| ≤ 1 (within 1 SD) 1 < |z| ≤ 2 |z| > 2 (outlier)
Additional Statistics
Coefficient of Variation (CV)
29.0957%
Relative variability = (s / x̄) × 100
Standard Error of Mean (SEM)
1.8516
SEM = s / √n
95% Confidence Interval
[14.3708, 21.6292]
99% Confidence Interval
[13.2302, 22.7698]