Variance Calculator

About Variance Calculator

Variance is the average of squared deviations from the mean. It is the square of standard deviation.

How to use this calculator

1. Enter the numbers in your dataset, separated by commas or spaces.
2. Choose whether you want population variance, which divides by \(n\).
3. Click calculate to find the variance instantly.
4. Use the result to compare spread between different datasets or to understand consistency.

The formula explained

The formula \(\sigma^2 = \frac{\sum(x_i - \bar{x})^2}{n}\) computes population variance. It finds the average of the squared distances from each data value to the mean.

• \(\sigma^2\) = population variance
• \(x_i\) = the i-th data value
• \(\bar{x}\) = the mean of the dataset
• \(n\) = the number of data values

Step by step method

1. Find the mean of the data by adding all values and dividing by \(n\).
2. Subtract the mean from each data value, then square each difference.
3. Add the squared differences and divide by \(n\) to get the variance.

Worked example

Problem. Find the population variance of the dataset 2, 4, 6, 8.

1. First find the mean: \(\bar{x} = (2+4+6+8)/4 = 20/4 = 5\).
2. Find squared differences: \((2-5)^2 = 9\), \((4-5)^2 = 1\), \((6-5)^2 = 1\), \((8-5)^2 = 9\). Add them: \(9+1+1+9=20\).
3. Divide by \(n=4\): \(\sigma^2 = 20/4 = 5\).

Tips and common mistakes

• Variance is always nonnegative because the differences are squared.
• Do not confuse variance with standard deviation, standard deviation is the square root of variance.

Frequently asked questions