Average & Statistics Calculator

Mean, Median, and Mode Explained

These three "measures of central tendency" each describe the middle of a data set in a different way, and they can tell very different stories.

• Mean is the arithmetic average — add all the values and divide by how many there are. It's the most common average but is sensitive to outliers.
• Median is the middle value when the numbers are sorted. With an even count, it's the average of the two middle values. The median resists outliers, which is why it's used for things like household income.
• Mode is the value that appears most often. A data set can have one mode, several modes, or none.

Why the Mean and Median Can Differ

When a data set is symmetrical, the mean and median are close. When it's skewed by extreme values, they diverge. Consider salaries of 30k, 35k, 40k, 45k, and 500k: the mean is 124k, but the median is 40k. The median far better represents a "typical" value here, which is why choosing the right average matters.

Range and Spread

The range — the largest value minus the smallest — is the simplest measure of how spread out your data is. A small range means the values cluster tightly; a large range means they're widely dispersed. For a fuller picture of spread, statisticians also use variance and standard deviation, but range is the quickest gauge.

Common Uses

• Averaging test scores, grades, or survey responses
• Finding typical values in sales, prices, or measurements
• Summarizing experiment or sports statistics
• Quick data checks before deeper analysis

Frequently Asked Questions

How do I calculate the mean?

Add up all the numbers and divide by how many numbers there are. For 4, 8, and 12, the mean is (4 + 8 + 12) ÷ 3 = 8.

What is the difference between mean and median?

The mean is the arithmetic average of all values, while the median is the middle value when the data is sorted. The median is more reliable when the data has outliers.

Can a data set have more than one mode?

Yes. If two or more values tie for the most frequent, the set is multimodal and has multiple modes. If every value appears once, there is no mode.

What is the range?

The range is the difference between the largest and smallest values. It's a quick measure of how spread out the data is.