Sample Variance vs Population Variance (original) (raw)
Last Updated : 6 Feb, 2026
Sample and Population variance are two essential measures in statistics used to quantify the spread or variability of data points in a dataset. Population variance measures how spread out the values are in an entire group (or population). On the other hand,sample variance is used when we have only a part of the group (a sample) and want to estimate the variance of the whole group.
Variance
Variance is a statistical measure that represents the degree of spread or dispersion in a set of values. In other words, it quantifies how much the numbers in a dataset differ from the mean (average) of the dataset. It helps us understand the spread or variability in our data.
- Sample Variance
- Population Variance
Differences Between Sample and Population Variance
| **Aspect | Sample Variance ( s2 ) | Population Variance ( σ2 ) |
|---|---|---|
| **Definition | Measure of dispersion in a sample | Measure of dispersion in an entire population |
| **Formula | s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2 | \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2 |
| **Mean Used | Sample mean (\bar{x}) | Population mean (μ) |
| **Denominator | n − 1 (degrees of freedom) | _N (total number of data points) |
| **Purpose | Estimates the population variance from a sample | Measures the true variance of the population |
| **Bias Adjustment | Dividing by n − 1 corrects the bias in estimation | No bias adjustment needed, uses entire population data |
| **Usage | When only a subset of the population is available | When the entire population data is available |
| **Data Set | Sample data (a subset of the population) | Population data (all data points in the population) |