What are the sources for these average calculations?

Mean, median, and mode follow OpenStax Introductory Statistics 2e, section 2.5, Measures of the Center of the Data: https://openstax.org/books/introductory-statistics-2e/pages/2-5-measures-of-the-center-of-the-data The range is the largest value minus the smallest value.

Average Calculator

Enter a list of numbers. You get the mean, the median, the mode, and the range.

Smart Tips

• Mean is the arithmetic average: add the numbers and divide by how many there are.

• Median is the middle of the sorted list. With an even count, average the two middle numbers.

• Mode is the most frequent value. Two values can tie. If nothing repeats, there is no mode.

• Range is the largest value minus the smallest. It is not a test score.

The Formula

mean = Σx / n range = max − min

mean Arithmetic mean
Sum divided by the count

median Middle of the ordered list
Average the two middle values when n is even

mode Most frequent value
Every value that shares the highest frequency

range Spread of the extremes
Largest minus smallest

A single number is its own mean, median, and mode, and its range is 0. If every value appears once and there is more than one number, the mode is reported as none.

Key Insights

Mean moves with outliers

One very large or very small number pulls the mean. The median stays with the middle of the ordered list.

More than one mode

If two values share the highest frequency, both are modes. OpenStax calls that bimodal.

Not a grade tool

Course averages and GPA live on their own pages. This list is just numbers.

Range is one subtraction

It ignores everything between the smallest and largest values.

Frequently Asked Questions

On this page, average means the arithmetic mean. Add the numbers and divide by how many there are.

Sort the numbers. If the count is odd, the median is the middle value. If the count is even, it is the mean of the two middle values.

Both are modes. A data set with two modes is bimodal. If nothing repeats and there is more than one number, the page reports no mode.

The largest value minus the smallest value. It is not a grade range and it is not a GPA.

Yes. One extreme number pulls the mean. The median depends only on the middle of the ordered list, so it does not follow that extreme value.

Mean, median, and mode follow OpenStax Introductory Statistics 2e, section 2.5, Measures of the Center of the Data. The range is the largest value minus the smallest value.

Responsive Ad Space

Mean

Enter values to calculate

Median

Mode

Range

Note:Mean, median, and mode describe the center of this list. Range is only the gap between the smallest and largest values. Grades and GPA are separate tools.