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 |
| Mean Used | Sample mean () | 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) |
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