Variance is an essential component of statistics and represents the variability of a data series about its mean. In this article, you will have an online calculator to obtain the variance and its calculation procedure at your disposal.
Variance Calculator
What is variance?
Variance is a measure of dispersion that evaluates how far each number in a data set is from its average. The variance is equal to the square of the standard deviation.
The formulas for calculating population and sample variance are given below:
(a) Population Variance:
(b) Sampling Variance:
Where:
- σ2: Population Variance.
- s2: Sampling Variance.
- x̄: Mean.
- N: Number of evaluated values.
- xi: Each one of the values.
Variance plays a central role in statistics, in topics such as descriptive statistics, hypothesis testing, statistical inference, Monte Carlo sampling, etc.
How to use the online variance calculator?
To use the online variance application, you should follow the steps below:
- Select the decimal separator and the data separator.
- Enter the values of the data set.
- Click on Solve.
- At the bottom of the form, you will be able to visualize the variance calculation procedure.
An example is shown below:
Example of variance calculation
Calculate the sample and population variance of the following data: 10, 12, 13, 16, 16, 9, 8, 8, 12, 8, 6, 16.
Solution
We record the data set:
Pressing the Solve button will show the procedure:
Population Variance: 11.4722
Sample Variance: 12.5152
Population Standard Deviation: 3.3871
Sample Standard Deviation: 3.5377
Mean: 11.1667
Count of Data: 12
According to the data of the problem we have:
- Σxᵢ = 110
- NÂ =Â 10
- x̄ = 110/10 = 11
| xi | xi – xÌ„ | (xi – xÌ„)2 |
|---|---|---|
| 10 | -1.1667 | 1.3612 |
| 12 | 0.8333 | 0.6944 |
| 13 | 1.8333 | 3.361 |
| 16 | 4.8333 | 23.3608 |
| 16 | 4.8333 | 23.3608 |
| 9 | -2.1667 | 4.6946 |
| 8 | -3.1667 | 10.028 |
| 8 | -3.1667 | 10.028 |
| 12 | 0.8333 | 0.6944 |
| 8 | -3.1667 | 10.028 |
| 6 | -5.1667 | 26.6948 |
| 16 | 4.8333 | 23.3608 |
| Σxáµ¢ = 134 | xÌ„ = 134/12 = 11.1667 | Σ(xáµ¢ – xÌ„)² = 137.6668 |
At the bottom of the solution, you will find the option to copy the link to the problem to see the calculated results without re-entering the data. You can share this link with a colleague.
Finally, you can calculate other measures of dispersion and central tendency using the following options:
- Online application of the average deviation.
- Online calculator for standard deviation.
- Online calculator for mean, median, mode, and range.
Final Reflection
Our variance calculator is an effective tool for students learning statistics and looking for a way to measure variance. This tool will help you better understand the concept of this metric.
