Three different "averages"
For the list 12, 15, 9, 22, 15, 18: the mean is 91 ÷ 6 = 15.17; the median is the average of the two middle values (15 and 15) = 15; the mode is 15, appearing twice. With an even count there's no single middle number, so the median averages the two central ones.
Which average should you use?
- Mean — the default for symmetric data: test scores, temperatures, measurements. Every value influences it, which is both its strength and its weakness.
- Median — the honest choice for skewed data: incomes, house prices, response times. One billionaire moving into town changes the mean income dramatically, the median barely at all.
- Mode — for categories and discrete choices: the most common shoe size sold, the most frequent survey answer. It's the only average that works for non-numeric data.
Watch out for outliers
The list 10, 12, 11, 13, 300 has a mean of 69.2 — describing precisely none of its members. The median, 12, tells the real story. When mean and median disagree sharply, the data is skewed or contains outliers, and that disagreement is itself useful information. For spread, see the standard deviation calculator.
Frequently asked questions
What's the difference between mean and average?
In everyday speech 'average' means the arithmetic mean — sum divided by count. Technically, mean, median, and mode are all averages (measures of central tendency); this calculator reports each so you can choose.
When is the median better than the mean?
Whenever a few extreme values could mislead: salaries, home prices, wait times. 'Median household income' is the standard statistic precisely because top earners drag the mean upward.
Can a list have no mode, or several modes?
Both. If every value appears once, there is no mode. If two or more values tie for most frequent, the list is multimodal — 1, 2, 2, 3, 3 has modes 2 and 3. The calculator lists them all.
How do I calculate a weighted average?
Multiply each value by its weight, sum those products, and divide by the total weight. Course grades work this way — our grade calculator does weighted averages directly.
Does the order of numbers matter?
Not for any statistic here — mean, median, mode, and range are all order-independent. The calculator sorts internally to find the median, so paste your data in any order.