Standard Deviation Calculator
Compute the standard deviation and variance for a dataset (population or sample).
Enter Data
Understanding Standard Deviation and Variance
Standard deviation and variance are key measures of data dispersion, indicating how spread out the numbers in a dataset are from the mean.
Formulas:
- Mean (&bar;x): Σxi / n
- Variance (σ2 or s2):
- Population: Σ(xi - μ)2 / N
- Sample: Σ(xi - &bar;x)2 / (n - 1)
- Standard Deviation (σ or s): √Variance
Where N is population size, n is sample size, μ is population mean, &bar;x is sample mean.
Standard Deviation Examples
| Dataset | Mean | Variance (Sample) | Std Dev (Sample) |
|---|---|---|---|
| 1, 2, 3, 4, 5 | 3 | 2.5 | 1.5811 |
| 10, 10, 10, 10 | 10 | 0 | 0 |
| 1, 5, 10, 15, 19 | 10 | 57.5 | 7.5829 |
Frequently Asked Questions
What is standard deviation?
Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
How is standard deviation calculated?
To calculate standard deviation: 1. Find the mean of the data set. 2. Subtract the mean from each data point and square the result. 3. Sum all the squared differences. 4. Divide the sum by the number of data points (for population standard deviation) or by (number of data points - 1) for sample standard deviation. 5. Take the square root of the result.
What is variance?
Variance is the average of the squared differences from the mean. It is a measure of how far each number in the set is from the mean. Standard deviation is simply the square root of the variance.