Variance and Covariance
Variance of the data set defines the volatility of all the values of the data set with respect to the mean value of the data set. Covariance tells us how the random variables are related to each other and it tells us how the change in one variable affects the change in other variables.
Covariance can be positive or negative, the positive covariance signifies that both variables are moving in the same direction with respect to the mean value whereas, negative covariance signifies that both variables are moving in opposite directions with respect to the mean value.
For two random variables x and y where x is the dependent variable and y is the independent variable the covariance is calculated using the formula mentioned in the below attached image.
Variance
Variance is a measurement value used to find how the data is spread concerning the mean or the average value of the data set. It is used to find how the distribution data is spread out concerning the mean or the average value. The symbol used to define the variance is σ2. It is the square of the Standard Deviation.
The are two types of variance used in statistics,
- Sample Variance
- Population Variance
The population variance is used to determine how each data point in a particular population fluctuates or is spread out, while the sample variance is used to find the average of the squared deviations from the mean.
In this article, we will learn about Variance (Sample, Population), their formulas, properties, and others in detail.
Table of Content
- What is Variance?
- Variance Definition
- Types of Variance
- Variance Symbol
- Variance Example
- Variance Formula
- Sample Variance Formula
- Population Variance Formula
- Variance Formula for Grouped Data
- Variance Formula for Ungrouped Data
- Formula for Calculating Variance
- How to Calculate Variance?
- Variance and Standard Deviation
- Variance and Covariance
- Variance Properties
- Examples on Variance Formula
- Summary – Variance
- FAQs on Variance