Calculate variance, standard deviation, and coefficient of variation for your data set. Supports both sample and population variance with step-by-step solutions.
Sample Variance
27.4286
s^2
Standard Deviation
5.2372
s
Sample variance uses n-1 (Bessel's correction) to provide an unbiased estimate when your data is a sample from a larger population.
Sample Variance
27.4286
Standard Deviation
5.2372
Mean
18.0000
Coefficient of Variation
29.10%
Min
10
Max
23
Range
13
Mean = Sum of all values / Count
Mean = 144.00 / 8
Mean = 18.0000
| Value (x) | x - Mean | (x - Mean)^2 |
|---|---|---|
| 10 | -8.0000 | 64.0000 |
| 12 | -6.0000 | 36.0000 |
| 23 | +5.0000 | 25.0000 |
| 23 | +5.0000 | 25.0000 |
| 16 | -2.0000 | 4.0000 |
| 23 | +5.0000 | 25.0000 |
| 21 | +3.0000 | 9.0000 |
| 16 | -2.0000 | 4.0000 |
| Sum | - | 192.0000 |
Sample Variance (s^2) = Sum of squared deviations / (n - 1)
s^2 = 192.0000 / (8 - 1)
s^2 = 192.0000 / 7
s^2 = 27.4286
Standard Deviation = sqrt(Variance)
s = sqrt(27.4286)
s = 5.2372
Red dashed line shows the mean (18.0000). Bars further from the line indicate larger deviations.
Use when estimating from a sample of a larger population
Use when you have all data points in the population
sigma^2 = Sum(x - mu)^2 / N
Divide by total count N
s^2 = Sum(x - x-bar)^2 / (n-1)
Divide by n-1 (Bessel's correction)
SD = sqrt(Variance)
Same units as original data
CV = (SD / Mean) x 100%
Relative variability measure
Sample Variance
27.4286
Standard Deviation
5.2372
Variance measures how spread out data is from the mean. Population variance: sigma-squared = Sum of (x - mu)^2 / N. Sample variance: s^2 = Sum of (x - x-bar)^2 / (n-1). Standard deviation is the square root of variance. Use population variance when you have all data points; use sample variance when working with a sample from a larger population (dividing by n-1 corrects for bias).
Variance is a statistical measure of the spread or dispersion of a set of data points around their mean. It quantifies how much the values differ from the average. A low variance indicates that data points are clustered close to the mean, while a high variance indicates data is spread out. Variance is the average of squared deviations from the mean, and standard deviation is its square root, expressing spread in the original data units.
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Variance measures how spread out data is from the mean. Population variance: sigma-squared = Sum of (x - mu)^2 / N. Sample variance: s^2 = Sum of (x - x-bar)^2 / (n-1). Standard deviation is the square root of variance. Use population variance when you have all data points; use sample variance when working with a sample from a larger population (dividing by n-1 corrects for bias).
Variance measures how spread out data is from the mean. It is calculated as the average of squared deviations from the mean. A variance of 0 means all values are identical; higher variance means more spread.
Population variance divides by N (total count) when you have all data points. Sample variance divides by n-1 (called Bessel's correction) to provide an unbiased estimate when working with a sample from a larger population.
Standard deviation is the square root of variance. While variance is in squared units, standard deviation is in the same units as the original data, making it easier to interpret and compare with the mean.
Coefficient of Variation (CV) = (standard deviation / mean) x 100%. It expresses variability as a percentage of the mean, allowing comparison of variability between datasets with different scales or units.
Use population variance when you have data for the entire population (all possible values). Use sample variance when you have a sample and want to estimate the variance of the larger population. Most real-world applications use sample variance.
Last updated: 2025-01-15
Sample Variance
27.4286
s^2
Standard Deviation
5.2372
s