Variance Calculator

Variance, σ2
Variance, σ2 (Sample)

What is Variance?

Variance is defined as one of the measures of dispersion, which means the measure of by how much numbers in data set possibly differ from mean of values. It shows the average square of deviations taken from their means. By taking the square of deviations it ensures that negative and positive deviations do not cancel each other out.

Why to use Variance Calculator?

The Variance Calculator is used for calculating the variance (either sample or population) of a set of values. The variance is to calculate how distantly available a set of numbers is from the mean of the data set. If numbers are distantly available within the data set, it shows high variance. If numbers are closely available within the data set, it shows low variance. A variance of 0 showed that all numbers are identical within the data set. If there is any non-zero value then variance will be a positive number.

What is Sample Variance?

How varied a sample is calculated by Sample Variance (σ²(sample)). A set of data as a data sample is collected from the population. Usually, the population is very large and complete counting of all values is impossible. Mainly sample is taken from a population with manageable size, say 2,000, and that data is used for calculations. Following variance formula is used for sample variance:

$$σ^2\;\text{(Sample)}\;=\;\frac{\sum x^2\;-\;\frac{(\sum x)^2}{N}}{N-1}$$

What is Population Variance?

How data points in a particular population are spread identified by population variance (σ2). This is calculated as the average of distances in the population from each data point to mean square. Following variance formula is used for population variance:

$$σ^2\;=\;\frac{\sum x^2\;-\;\frac{(\sum x)^2}{N}}{N}$$

How to Calculate Variance using Variance Calculator?

Follow the below steps for using this calculator

1. First, enter the values in the white shaded box. You may also copy/paste data in the white shaded box. Values must be numeric and separated by commas. A comma must be used to separate the values otherwise calculator shows an error “Please match the required format”.
2. After entering values you may click on the “Calculate” button to execute the computation.
3. The calculator will calculate the resultant variance and displayed results for both Variance (σ2) and Variance σ2 (Sample).

How Variance Calculator works?

This calculator calculates answer quickly and here is a step-by-step guide on how Variance Calculator calculates the Variance (σ2):

• Variance Calculator uses the following formula to calculate the Variance(σ2).

$$σ^2\;=\;\frac{\sum x^2\;-\;\frac{(\sum x)^2}{N}}{N}$$

• Step 1: Determine all possible outcomes

This calculator calculates the variance from set of values. First step it uses is to take square of all the values available in the entire population:

x x2
400 160000
270 72900
200 40000
350 122500
170 28900
• Step 2: Calculate the Mean

Then calculate the sum of all values, ∑x

$$\sum x\;=\;1390$$

• Take the square of answer and divide that value by size of population.

$$\frac{(\sum x)^2}{N}\;=\;\frac{1390^2}{5}\;=\;\frac{1932100} {5}\;=\;386420$$

• Then calculate the sum of all the square values, ∑x2

$$\sum x^2\;=\; 424300$$

• Subtract,

$$\frac{\sum x^2\;-\;(\sum x)^2}{N}\;=\;424300–386420\;=\;37880$$

• Step 3: Calculate Variance

For Variance, divide the answer with size of population,

$$σ^2\;=\;\frac{\sum x^2\;-\;\frac{(\sum x)^2}{N}}{N}\;=\;\frac{37880} {5}=7576$$

So the Variance is 7576.

Similar steps were taken for calculating Sample Variance, only the last step is varied according to formula.

$$σ^2\;\text{(Sample)}\;=\;\frac{\sum x^2\;-\;\frac{(\sum x)^2}{N}}{N-1}$$

For Variance, divide the answer with one less than the size of the population,

$$σ^2\;\text{(Sample)}\;=\;\frac{\sum x^2\;-\;\frac{(\sum x)^2}{N}}{N-1}\;=\;\frac{37880}{4}\;=\;9470$$

So the Variance is 9470.

Calculating the variance includes square deviations, so the units are not the same as units entered in the input field for the values variance calculator calculates. For example, if numbers entered in the input field are in millimeters, the resultant variance answers will be in square millimeters. The unit is square of entered values in the resultant value.

Uses

Variance calculation is important and vital for many statistical and probability purposes and provides other ways to evaluate our results simply and easily. For photoelectric we have average values for current, voltage, etc. From this calculator, we calculate how much variance a specific current, voltage, etc is from its normal value. This is also useful for many other statistical purposes.

Properties

The Variance has two main properties:

• It never shows negative results because every time squared values are used for taking the mean and therefore results are either positive or zero.
• Variance has squared units.