Calculator Tools
Standard Deviation Calculator
Calculate sample and population standard deviation, variance, mean, median, range, quartiles, and outliers with a step by step formula breakdown.
Standard deviation (sample)
s = 3.02765
Variance: 9.166667 · Mean: 14.5 · n: 10
Count (n)
10
Sum
145
Mean (x̄)
14.5
Median
14.5
Min
10
Max
19
Range
9
Q1
12
Q3
17
IQR
5
Sum of squared deviations
82.5
Variance (sample)
9.166667
Outliers (1.5 × IQR rule)
(none)
Step by step calculation
- Step 1: Find the meanx̄ = (145) / 10 = 14.5
- Step 2: Subtract the mean from each value, then square itSum of squared deviations Σ(xᵢ − x̄)² = 82.5
- Step 3: Divide by 9 (n − 1 for sample, Bessel's correction) to get the variances² = 82.5 / 9 = 9.166667
- Step 4: Take the square root to get the standard deviations = √9.166667 = 3.02765
Per value working
Squared distance from the mean for each data point.
| Value (xᵢ) | xᵢ − x̄ | (xᵢ − x̄)² |
|---|---|---|
| 12 | -2.5 | 6.25 |
| 15 | 0.5 | 0.25 |
| 11 | -3.5 | 12.25 |
| 18 | 3.5 | 12.25 |
| 14 | -0.5 | 0.25 |
| 17 | 2.5 | 6.25 |
| 13 | -1.5 | 2.25 |
| 16 | 1.5 | 2.25 |
| 19 | 4.5 | 20.25 |
| 10 | -4.5 | 20.25 |
| Sum of squared deviations | 82.5 | |
How to use
- Paste or type your numbers into the data set area, separated by commas, spaces, semicolons, or newlines.
- Pick Sample (s, divides by n − 1) if your numbers are a sample of a larger group, or Population (σ, divides by n) if the data covers every member.
- Read the headline standard deviation, the supporting stats grid, and the four step formula breakdown.
- Use Copy summary to grab the full report, or Load sample to see how a realistic data set is calculated.
About this tool
Standard Deviation Calculator measures how spread out a data set is around its mean. Paste a list of numbers separated by commas, spaces, or newlines and the calculator returns the sample standard deviation (s, divides by n − 1 using Bessel's correction), the population standard deviation (σ, divides by n), the corresponding variances, the mean, median, range, minimum, maximum, first and third quartiles, the interquartile range, and any outliers detected by the 1.5 × IQR rule. Toggle between sample and population at any time. The page also shows a four step working that walks through the formula: mean, sum of squared deviations, variance, then square root, plus a per value table that lists each data point, its deviation from the mean, and its squared deviation for data sets up to 30 numbers. Useful for statistics homework, lab reports, A/B test analysis, finance volatility checks, quality control, and any time you need to summarise the dispersion of a set of measurements. Every calculation runs in your browser, so your numbers stay on your device.
Free to use. Works in your browser. No signup, no login.
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