Variance is a very important term in statistics, and in probability theory, it also plays an important role. Variance generally refers to the measurement of the scattered set of numbers or values that are spread out

from their average value.

The Variance was first introduced in 1918, and Mr Ronald Fisher gave the concept of this term. He wrote the concept of variance in his scientific paper which was published by the Royal Society of Edinburgh. In this article, we will study the basic definition of variance and its types, there is also an example section.

#### Definition of variance

“In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.”

#### Kinds of variance

There are two basic kinds of variance:

1. Sample variance

2. Population variance

#### 1. What are the sample and population?

**Sample**

Sample refers to a random collection of data from a large data (population) i.e. a factory produces 1000 bulbs

on daily basis and we want to check the quality of all bulbs then we will take 10 bulbs out of that 1000 (1 from every 100). The chances of error in the sample are more than in the population.

**Population**

The population data is the total number of relevant observations. It is typically larger than a sample, and the ratio of errors is very less as compared to the sample data i.e. in the above example, the total number of bulbs (1000) is the population. The population is always greater than the sample.

#### 2. Sample variance

The variance of sample data is represented by S^{2} and is given by:

– S^{2} is the variance of the sample data.

– x_{i} is the number of terms.

– x̅ is the mean of the sample data.

– n is the total terms.

#### 3. Population variance

The population variance is represented by σ2 and is given by:

– σ^{2} is the variance of the population data.

– x_{i} is the number of terms.

– µ is the population mean.

– N is the total terms.

#### How to calculate the variance?

There are some simple steps to calculate the variance of the sample and the population data, these steps are

as follows.

#### 4. Sample data variance calculation

The following steps will help you to calculate the variance of the sample data:

- First of all, find the mean of the given sample data i.e., x̅
- Find the difference between the values and the mean.
- Find the square of the difference.
- Sum up the squared values.
- The last step is to divide the calculated value by “n – 1” (for sample variance) to get the final answer.

#### 5. Population data variance calculation

You can calculate the variance of the population by using the following steps.

- First of all, find the mean of the given population data i.e., µ
- Find the difference between the values and the mean (deviation)
- Find the square of the difference.
- Sum up the squared values. (Sum of squares)
- Divide the calculated value by “N” (for population variance) to get the final answer.

Have a look at Solved Examples of Sample & Population Variance for better understanding.

#### Variance Calculator

A variance calculator can help you to get rid of these lengthy calculations and you will get a step-by-step solution to the problem.

#### Summary

In this article, we have studied the basic definition of variance, and the general history of this term. We have also read about the types of variances and the difference between the sample and the population. We have also gone through the method of finding the variance.

Improve your Skills with Meritstore! Click here.

## Add Comment