Variance Calculator

Determine variance for data sets quickly and effortlessly with our tool.

Variance Calculator

Data Set

Comma-separated numbers

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	Sample	Population
Variance	σ2 = 28.5	s2 = 24.9375
Standard Deviation	σ = 5.3385	s = 4.9937
Count	n = 8	n = 8
Mean	μ = 18.25	x̄ = 18.25
Sum of Squares	SS = 199.5	SS = 199.5

What is an Online Variance Calculator?

An Online Variance Calculator is a tool that helps you calculate the variance of a dataset. Variance is a statistical measurement that describes the spread or dispersion of a set of numbers. It represents how far each number in the dataset is from the mean (average) and, therefore, gives a sense of how much the values differ from the average value. Variance is the square of the standard deviation and is commonly used in fields such as statistics, finance, and data analysis.

The formula to calculate variance for a dataset is:

For population variance:

\sigma^2 = \frac{\sum{(x_i - \mu)^2}}{n}

For sample variance:

s^2 = \frac{\sum{(x_i - \bar{x})^2}}{n - 1}

Where:

$\sigma^2$ or $s^2$ is the variance,
$x_i$ represents each data point,
$\mu$ is the population mean, and $\bar{x}$ is the sample mean,
$n$ is the number of data points in the population or sample.

How to Use an Online Variance Calculator?

Access the Tool: Open a web browser and go to an online variance calculator tool.
Enter the Data: Input the dataset (the list of numbers) for which you want to calculate the variance. Usually, numbers are entered by separating them with commas, spaces, or line breaks.
Choose Population or Sample Variance (if applicable): Some calculators will prompt you to choose between calculating the population variance or the sample variance. For a sample, use $n-1$ in the denominator to account for sample error.
Click “Calculate” or “Compute”: After entering the data, click the "Calculate" button to compute the variance.
View the Result: The calculator will display the variance of the dataset. Some calculators may also display additional statistics such as the mean, standard deviation, or range of the data.

Frequently Asked Questions-

What is the difference between variance and standard deviation?
- Variance is the average of the squared differences from the mean, giving a measure of the spread of the data.
- Standard deviation is the square root of the variance and gives a more interpretable measure of spread in the same units as the original data.
How do I interpret a high or low variance?
- A high variance indicates that the data points are widely spread out from the mean, suggesting more variability in the data.
- A low variance means that the data points are clustered closely around the mean, indicating less variability.
Can online variance calculators handle large datasets?
Yes, most online variance calculators can handle large datasets, but there may be practical limits depending on the tool being used. Some calculators may allow you to upload data directly from a file, while others might have a limit on the number of values you can enter.
What happens if all values in the dataset are the same?
If all the values in the dataset are the same, the variance will be 0. This is because the data points do not deviate from the mean at all, and there is no variability or spread.
Why is the sample variance formula different from the population variance formula?
The sample variance formula uses $n-1$ in the denominator instead of $n$ to account for the fact that a sample may not perfectly represent the entire population. This adjustment, known as Bessel's correction, helps to reduce bias in estimating the population variance from a sample.