# Variance Calculator

Variance Calculator allows you to find the sample and population variance of a set of data. Also, you will learn the variance formula.

##### More Statistical Resources:
Z Table T Distribution Table Average Calculator

Variance Calculator is a free online tool where you can calculate the variance of a set of numbers. Just enter the data set and select the data type: Sample or Population. Lastly, press the "Calculate" button. As a result, you will get the variance value instantly. In addition, our tool gives Standard Deviation and Mean results.

Most importantly, our calculator saves your time as well as effort while you attempt to solve it on your own. So, you can make your calculations hassle-free and quicker using our tool.

### What is Variance?

Variance is a statistical measurement of the dispersion between numbers in a data set. In other words, it measures how far each element in a data set is from the mean value and thus from every other element in a data set.

The low variance indicates that the data is less spread out or is more tightly clustered around the mean. Whereas high variance indicates that the data values are more widely spread out from the mean.

Also, it is represented by this symbol: "σ2".

#### Variance Formula

##### Population Variance:

Where,
σ2 = Population variance
xi = Value of ith element
μ = Mean value of all elements
n = Number of elements

##### Sample Variance:

Where,
s2 = Sample variance
xi = Value of ith element
x̄ = Mean value of all elements
n = Number of elements

### How to Calculate Variance?

You can always use a variance calculator to calculate variance with ease and quickly. However, if you want to learn how to calculate it manually, then follow the steps below. Also, we will take an example to understand how to calculate variance.

#### Example:

Calculate the sample variance for the data set of 46 69 32 60 52 41.

#### Solution:

As we know that the sample variance formula is:

s2 = ∑(xi - x̄)2 / (N - 1)

Step 1: Firstly, calculate the mean(x̄) by adding up all the data points present in the dataset. Then divide them by the number of data points.

Mean (x̄) = (46 + 69 + 32 + 60 + 52 + 41) / 6 = 50

Step 2: Now subtract the mean value from each data point to obtain the individual deviation from the mean. As the mean is 50. So, subtract 50 from each data point.

ScoreDeviation from the mean
4646 - 50 = -4
6969 - 50 = 19
3232 - 50 = -18
6060 - 50 = 10
5252 - 50 = 2
4141 - 50 = -9

Step 3: Now find the square of each deviation from the mean to get the squared deviation.

Squared deviation
(-4)2 = 16
(19)2 = 361
(-18)2 = 324
(10)2 = 100
(2)2 = 4
(-9)2 = 81

Step 4: Lastly, add up all the squared deviation and divide it by the number of data points minus one. That is: (N-1) = (6-1) = 5.

(16 + 361 + 324 + 100 + 4 + 81) / 5 = 886/5 = 177.22

It is quite obvious that manual calculation can be very complex and time taking. Also, you can never be completely sure that the outcome of your manual calculations will be correct. Hence, the variance calculator is the best option in such conditions. It's free, fast, accurate, and offers multiple functionalities.

#### Features of Variance Calculator

• Simple UI: The simple and interactive user interface of this tool makes it easy to understand and use. All you need to do is enter the data, select the type of data and press the calculate button. As a result, the answer will be on your screen in seconds.
• Comprehensive: This tool lets you find out the population as well as sample variance. Therefore, you don't need to use other tools for different calculations.
• Fast and accurate: It gives you fast and 100% accurate results.
• Free for all: It's completely free to use for all users. Also, the tool does not include any type of hidden charges.
• No pre-requirement: The tool does not require you to log in or sign up or install anything to use it. Just open it online on your device and start using it.
• Additional functions: Besides variance, you can also find the standard deviation and mean.
• Compatibility and security: No data is stored or sent to the server. So, it's completely safe and secure to use. Moreover, you can use it on various devices like mobile, laptop, PC, tablet, etc. Also, our tool supports almost all browsers and operating systems.

### How to use Variance Calculator?

As we already discussed, the tool is straightforward and easy to use. Hence, you will never face any difficulty while using the calculator. Just follow the instructions below to use it.

1. Firstly, open the Variance Calculator on any device that has an active internet connection and browser support.
2. Then, enter the set of values or the data you want to calculate the variance for. Make sure that the entered data set is in a proper format. The right format is: 3 5 7 8 10 or 3, 5, 7, 8, 10.
3. Now, select the data type: Sample or Population.
4. Lastly, press the "Calculate" button.
5. As a result, our tool will display the variance result along with standard deviation and mean on your device's screen in a second.
6. You can press the "Reset" button to clear all the input as well as output fields.

### FAQs

Sample Variance Formula:
s2 = ∑(xi - x̄)2 / (N - 1)

Population Variance Formula:
σ2 = ∑(xi - μ)2 / N

Yes, you can find out the variance of both positive and negative values.

Yes, our tool supports decimal values. So, you can include it in the data set.

Yes, our tool is all device friendly. So, you can use it on any type of device. Such as mobile, iPad, laptop, or desktop.

Yes, our tool gives you the standard deviation, mean, and variance results.