Variance (Sample) Calculator
The square of the standard deviation.
Formula first
Overview
Sample variance measures the average squared deviation of data points from their mean within a specific subset of a population. It utilizes Bessel's correction, dividing by n - 1, to provide an unbiased estimate of the true population variability.
Symbols
Variables
s^2 = Sample Variance, \Sigma(x-\bar{x})^2 = Sum of Squares, n = Sample Size
Apply it well
When To Use
When to use: This formula is used when you are working with a sample of data rather than an entire population. It is applicable for interval or ratio data in psychological research where quantifying the spread of scores is necessary for inferential testing.
Why it matters: Variance serves as the mathematical foundation for more complex statistical analyses like ANOVA and regression. In psychology, understanding variance helps researchers distinguish between meaningful experimental effects and random individual differences.
Avoid these traps
Common Mistakes
- Reporting variance as the final measure of spread instead of standard deviation.
- Dividing by n instead of n-1 for sample data.
One free problem
Practice Problem
A clinical psychologist measures the stress levels of 10 patients. The calculated Sum of Squares (SS) for their scores is 180. What is the sample variance?
Solve for:
Hint: Divide the Sum of Squares by the degrees of freedom, which is n - 1.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Variance
- Wikipedia: Bessel's correction
- Britannica: Variance
- Gravetter, F. J., Wallnau, L. B., Forzano, L. B., & Witnauer, J. E. (2021). Statistics for the Behavioral Sciences (11th ed.). Cengage.
- AQA A-level Psychology Specification