Standard Deviation Calculator
Calculate standard deviation, variance, z-scores, and confidence intervals for any dataset.
Standard Deviation (σ)
5.9025
Variance (σ²)
34.8400
Mean (x̄)
86.60
Coeff. of Variation
6.82%
Std Error
1.8665
Count (N)
10
95% CI
82.94 - 90.26
Z-Scores
85-0.271
90+0.576
78-1.457
92+0.915
88+0.237
76-1.796
95+1.423
82-0.779
89+0.407
91+0.745
Frequently Asked Questions
What is standard deviation?+
Standard deviation measures how spread out data is from the mean. A low SD means data points cluster near the average. A high SD means they're widely spread. It's expressed in the same units as the data.
Population vs sample standard deviation?+
Population SD (σ) divides by N — use when you have ALL data points. Sample SD (s) divides by N-1 — use when you have a sample from a larger population. The N-1 correction (Bessel's) makes sample SD an unbiased estimator.
What is a z-score?+
A z-score tells you how many standard deviations a value is from the mean. Z=0 means at the mean. Z=1 means 1 SD above. Z=-2 means 2 SDs below. About 68% of data falls within ±1 SD, 95% within ±2 SD.