Population Variance and Standard Deviation
Key differences between population variance and standard deviation are:
Aspect | Standard Deviation | Population Variance |
|---|---|---|
Definition | Measures the spread of data points in a population from the population mean. | Measures the dispersion of data points in a population from the population mean. |
Formula | [Tex]\sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i – \mu)^2[/Tex] | [Tex]\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i – \mu)^2}[/Tex] |
Units | Squared units of the original data (e.g., square meters, square dollars). | Same units as the original data (e.g., meters, dollars). |
Bias Correction | Uses N in the denominator. | Uses N−1 in the denominator. |
Representation | σ2 | σ |
Sensitivity to Outliers | Less sensitive, as it squares differences before averaging. | More sensitive, as it considers absolute differences. |
Population Variance
Population variance is a fundamental concept in statistics that quantifies the average squared deviation from the mean of a set of data points in a population. It is a measure of how spread out a group of data points is.
There are two types of data available, namely, ungrouped and grouped data. Thus, there are two formulas to calculate the population variance. In this article, we will learn more about population variance, its formulas, and various associated examples.
Table of Content
- What is Population Variance?
- Formula of Population Variance
- Ungrouped Data
- Grouped Data
- Population Variance and Sample Variance
- Population Variance and Standard Deviation
- Solved Problems on Population Variance
- Practice Questions on Population Variance
- FAQs on Population Variance