Mean, median and mode: three kinds of average
The mean is what most people call "the average": add everything up and divide by how many numbers there are. The median is the middle value once the numbers are sorted — half the list is below it and half above. The mode is the value that appears most often. A list can have one mode, several, or none at all if every value appears once.
The range isn't an average; it measures spread. It's simply the largest value minus the smallest.
Which average should you use?
The mean uses every value, which makes it sensitive to outliers. Five salaries of $40,000, $45,000, $50,000, $55,000 and $400,000 have a mean of $118,000, which describes nobody in the group. The median, $50,000, is much more typical. That's why home prices and household incomes are usually reported as medians.
Use the mean when values are roughly balanced around the middle and you care about totals (average spending per day times days gives total spending). Use the median for skewed data such as incomes, prices or wait times. Use the mode for categories or repeated values, such as the most common shoe size sold.
Getting the steps right by hand
Always sort the numbers before finding the median; the middle of an unsorted list means nothing. With an even count there are two middle values, and the median is their mean, so it may be a number that isn't in your list.
Watch for typing errors: one misplaced decimal point (45 instead of 4.5) can move the mean a long way while barely changing the median. This calculator adds your numbers as exact decimals, so you won't see artifacts like 0.1 + 0.2 = 0.30000000000000004 that appear in some software.
Formulas
Mean = (x₁ + x₂ + … + xₙ) ÷ nMedian = the middle value of the sorted list (odd n), or the mean of the two middle values (even n)Mode = the value(s) that occur most oftenRange = largest value − smallest value- x₁ … xₙ are your numbers
- n is how many numbers there are (the count)
Worked example: 7, 3, 9, 3, 5, 12, 3, 6
- Count: 8 numbers. Sum: 7 + 3 + 9 + 3 + 5 + 12 + 3 + 6 = 48.
- Mean = 48 ÷ 8 = 6.
- Sorted: 3, 3, 3, 5, 6, 7, 9, 12. The count is even, so the median is the average of the 4th and 5th values: (5 + 6) ÷ 2 = 5.5.
- Mode: 3 appears three times, more than any other value, so the mode is 3.
- Range: 12 − 3 = 9.
Frequently asked questions
Is the average the same as the mean?
In everyday use, yes: "average" usually means the arithmetic mean. Strictly, the median and mode are averages too — they're all ways of describing a typical value.
How do I find the median of an even number of values?
Sort the list and average the two middle values. For 2, 4, 6, 10 the middle values are 4 and 6, so the median is (4 + 6) ÷ 2 = 5.
Can there be more than one mode?
Yes. In 1, 2, 2, 3, 3, 4, both 2 and 3 appear twice, so the list has two modes (it's bimodal). If every value appears once, there is no mode.
Why is my mean so different from my median?
Usually because of outliers or skew. A few very large values pull the mean up but barely move the median. For $40,000, $45,000, $50,000, $55,000 and $400,000, the mean is $118,000 but the median is $50,000.
How do I average numbers that have different weights?
Multiply each value by its weight, add those products, and divide by the total of the weights. This page treats every number equally; to weight a value, you can list it more than once.
Sources
Last reviewed for 2026. How we calculate.