Variance Properties
Variance is widely used in Mathematics, Statistics, and other branches of science for a variety of purposes. Variance has various properties which are widely used for solving various problems. Some of the basic properties of the variance are,
- Variance of the data set is the non-negative quantity and the zero value of variance signifies that all the values of the data set are equal.
- A higher value of the variance tells us that all the data values of the data set are widely dispersed, i.e. they are far away form the mean value of the data set.
- A lower value of the variance tells us that all the data values of the data set are close to each other, i.e. they are very close form the mean value of the data set.
For any constant ‘c’
- Var(x + c) = Var(x)
where x is a random variable
- Var(cx) = c2
where x is a random variable
Also, if a and b are the constant value and x is a random variable then,
- Var(ax + b) = a2
For independent variables x1, x2, x3…,xn we know that,
- Var(x1 + x2 +……+ xn) = Var(x1) + Var(x2) +……..+Var(xn)
People Also Read:
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
Contact Us