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Standard Deviation Calculator
Calculate mean, variance, and standard deviation.
Dataset Configuration
Summary Statistics
Standard Deviation (σ or s)
2.138090
Data Distribution Chart
Worked Deviation Proof
| Index (i) | Value (xᵢ) | Deviation (xᵢ - mean) | Squared Deviation (xᵢ - mean)² |
|---|---|---|---|
| #1 | 2 | -3.0000 | 9.0000 |
| #2 | 4 | -1.0000 | 1.0000 |
| #3 | 4 | -1.0000 | 1.0000 |
| #4 | 4 | -1.0000 | 1.0000 |
| #5 | 5 | +0.0000 | 0.0000 |
| #6 | 5 | +0.0000 | 0.0000 |
| #7 | 7 | +2.0000 | 4.0000 |
| #8 | 9 | +4.0000 | 16.0000 |
| Sum (Σ) | 40.0000 | 0.0000 | 32.0000 |
Statistical Equations Filled with Coordinates:
1. Compute Mean:
\(\mu = \frac{\sum x_i}{N} = \frac{40.0000}{8} = 5.000000\)
2. Compute Variance:
\(s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{32.0000}{8 - 1} = \frac{32.0000}{7} = 4.571429\)
3. Compute Standard Deviation:
\(s = \sqrt{s^2} = \sqrt{4.571429} = 2.138090\)
Formula
Standard Deviation and Variance Equations
s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}Calculates sample standard deviation using Bessel’s correction (n - 1) to account for sampling bias.
Step by step
How the calculation works
- 1Input your numerical dataset, separating values using commas, spaces, or newlines.
- 2Toggle between "Sample" mode (estimating a population) and "Population" mode (complete dataset).
- 3Review the mean, variance, standard deviation metrics, scatter plots, and the worked step-by-step deviations table.
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