Standard Deviation Calculator
Enter up to 20 numbers to calculate mean, median, mode, variance, and standard deviation.
8 numbers entered
Step-by-Step: Population Variance
Mean = (4 + 7 + 13 + 2 + 1 + 9 + 4 + 8) / 8
= 6
Squared diffs:
(4 − 6)² = 4
(7 − 6)² = 1
(13 − 6)² = 49
(2 − 6)² = 16
(1 − 6)² = 25
(9 − 6)² = 9
(4 − 6)² = 4
(8 − 6)² = 4
Population Variance = sum / 8 = 14
Population SD = √14 = 3.741657
Sample Std. Deviation
4
Population SD: 3.741657
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Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population SD (σ) is used when your data represents an entire population. Sample SD (s) is used when your data is a sample — it divides by (n−1) instead of n to correct for bias, making it a better estimator of the population SD.
What does standard deviation tell you?
Standard deviation measures how spread out values are from the mean. A low SD means data points are close to the mean; a high SD means they are spread out. About 68% of data falls within 1 SD of the mean in a normal distribution.
How is variance related to standard deviation?
Variance is the average of squared differences from the mean. Standard deviation is simply the square root of variance. SD is in the same units as the original data, making it easier to interpret.