Variance
What is Variance in Statistics?
Variance is defined as the spread of the values of the data set with respect to the mean value of the data set. The variance of the data set tells the extent to which the values in a particular data set spread from the mean value.
What is the Symbol of Variance?
We use the symbols σ2, s2, and Var(x) to denote the Variance of the data set.
What is the Formula of Variance?
Variance of the data set is calculated using the formula,
σ2 = E[( X – μ)2]
What does Variance tell?
Variance is used to find the extent of the spread of the data i.e. it tells us how the values in a data set are spread out with respect to the mean value. For the larger value of variance, the values are widely spread with respect to the mean value whereas with respect to the smaller value of variance, the values are closely spread with respect to the mean value
What is the Relation between Variance and Standard Deviation?
For the given data set variance of the data set is the square of the standard deviation of that data set. This relation is expressed as,
Variance = (Standard Deviation)2
How Do You Calculate Variance?
To calculate variance, you first find the mean (average) of the data set. Then, subtract the mean from each data point and square the result. Finally, average these squared differences.
Why is Variance Important?
Variance is crucial for understanding the distribution of data within a dataset. It helps in determining how spread out the data points are from the average value, indicating the variability or consistency within the data.
What is the Difference Between Variance and Standard Deviation?
While both variance and standard deviation measure data dispersion, the standard deviation is the square root of the variance. Standard deviation is expressed in the same units as the data, making it more interpretable for indicating the spread.
Can Variance be Negative?
No, variance cannot be negative. Since it is calculated as the average of the squared differences from the mean, the resulting value is always non-negative.
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