Standard Deviation Calculator
Standard deviation calculator
Spread from one value list.
InputsPopulation (N)8 valuesLive
Population SD
2
Population SD • n=8
Live update
N divisor
Mini chart
Variance
4
Count (n)
8
Advanced options
Count (n)
8
Mean
5
Variance
4
Median
4.5
Distribution
Histogram with mean ±1 SD band.
6/8 within ±1 SD
2Mean 59
Spread
75% lie within one SD
6/8 values are between 3 and 7.
Outliers
1 potential outlier
Fences: 1.75 to 7.75 • Values: 9
Steps and value table
σ = sqrt(sum((x - μ)^2) / N)- 1. Mean = 40 / 8 = 5
- 2. Sum of squared deviations = 32
- 3. Divide by 8 (N) = 4
- 4. Square root of variance = 2
| # | Value | Deviation | Squared | Z-score |
|---|---|---|---|---|
| 1 | 2 | -3 | 9 | -1.5 |
| 2 | 4 | -1 | 1 | -0.5 |
| 3 | 4 | -1 | 1 | -0.5 |
| 4 | 4 | -1 | 1 | -0.5 |
| 5 | 5 | 0 | 0 | 0 |
| 6 | 5 | 0 | 0 | 0 |
| 7 | 7 | 2 | 4 | 1 |
| 8 | 9 | 4 | 16 | 2 |
Formula
sigma = sqrt(sum((x - mean)^2) / N) s = sqrt(sum((x - mean)^2) / (N - 1)) Symbol legend
| Symbol | Meaning | Unit | Copy |
|---|---|---|---|
\sigma | Population standard deviation | same as x | |
s | Sample standard deviation | same as x | |
x_i | Each observed value | input unit | |
\mu | Population mean | input unit | |
\bar{x} | Sample mean | input unit | |
N | Number of observations | count |
- Use population mode when your dataset is the full population (N).
- Use sample mode when your dataset is a sample from a larger population (N - 1).
- The calculator accepts values separated by commas, spaces, semicolons, or new lines.
Example
Worked example: 2, 4, 4, 4, 5, 5, 7, 9
- 1 Mean = 5
- 2 Sum of squared differences = 32
- 3 Population variance = 32 / 8 = 4
- 4 Population standard deviation = sqrt(4) = 2
Population standard deviation is 2.
How
- Enter up to 20,000 numbers separated by commas, spaces, semicolons, or new lines.
- Choose sample or population mode.
- Review standard deviation, variance, quartiles, histogram, and potential outliers.
Avoid
- Choosing sample mode when the dataset is a full population.
- Including non-numeric values in the list.
- Forgetting that a single value cannot produce sample standard deviation.
FAQ
What is the difference between sample and population mode?
Sample mode divides by N - 1, while population mode divides by N.
Can I paste values with spaces instead of commas?
Yes. Spaces, commas, semicolons, and new lines are all supported.
Does this tool also return the mean?
Yes. It also returns variance, median, range, quartiles, coefficient of variation, and an IQR outlier check.
How many values can I analyze?
You can analyze up to 20,000 finite numeric values in one dataset.
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