Enter your dataset as comma-separated numbers to calculate both sample and population standard deviation. The Standard Deviation Calculator returns the standard deviation, variance, mean, count, and sum for your data — choose between Sample or Population mode using the toggle.
Standard Deviation
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Variance
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Mean (Average)
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Count (n)
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Sum
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Minimum
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Maximum
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Standard deviation is a statistical measure that quantifies how spread out values in a dataset are around the mean. A low standard deviation means data points cluster closely to the average, while a high standard deviation indicates the values are more widely dispersed.
Population standard deviation (σ) is used when you have data for an entire population and divides the sum of squared deviations by n. Sample standard deviation (s) is used when your data is a subset of a larger population and divides by n−1 (Bessel's correction) to produce an unbiased estimate.
For population SD: σ = √[Σ(xᵢ − μ)² / n]. For sample SD: s = √[Σ(xᵢ − x̄)² / (n−1)]. In both cases you subtract the mean from each value, square the result, sum those squares, divide by n or n−1, and then take the square root.
First, find the mean of your dataset. Then subtract the mean from each data point and square each result. Sum all the squared differences, divide by n (population) or n−1 (sample) to get the variance, and finally take the square root of the variance to get the standard deviation.
Variance is the average of the squared deviations from the mean. Standard deviation is simply the square root of the variance. Variance is expressed in squared units, which can be hard to interpret, while standard deviation is in the same units as the original data — making it more intuitive.
Standard deviation is useful any time you want to understand the spread or variability of a dataset — for example, in quality control, finance (measuring investment risk), academic testing, and scientific research. It's especially meaningful when comparing variability between two different datasets.
Type or paste your numbers into the Data Set field, separated by commas, spaces, or line breaks. For example: 10, 34, 23, 54, 9. The calculator accepts any mix of integers and decimal numbers, then computes all results automatically.
Dividing by n−1 instead of n (known as Bessel's correction) corrects the bias that arises when estimating a population's variance from a sample. Because a sample tends to underestimate spread, using n−1 produces a larger, more accurate estimate of the true population standard deviation.