Average Calculator — Mean, Median and Mode
This average calculator finds the three most common measures of central tendency for any set of numbers: the mean (arithmetic average), the median (middle value) and the mode (most frequent value). Just paste or type your data separated by commas, spaces or line breaks and the results update instantly, along with the count, sum, minimum, maximum and range. It is useful for students, teachers, researchers and anyone working with grades, prices, measurements or survey data.
Separate values with commas, spaces or line breaks.
Mean (average)
Median
Mode
Count
Sum
Minimum
Maximum
Range
The mean is the sum divided by the number of values. The median is the middle value of the sorted set. The mode is the value (or values) that appears most often; if no value repeats, there is no mode.
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How it works
The mean is the arithmetic average: add every value together and divide the total by how many values there are. The median is the middle value once the numbers are sorted from smallest to largest — when the count is even, it is the average of the two central values. The mode is the value that appears most often; a data set can have one mode, several modes, or no mode at all when every value occurs only once. The range is simply the largest value minus the smallest.
Mean, median and mode in one example
With the set 2, 3, 3, 8, 9 the three measures give different results. The mean spreads the total across every value, the median picks the number that sits right in the middle, and the mode looks at which value repeats the most. Seeing them side by side makes clear what each one measures and why they do not always agree:
| Measure | Value | How it is obtained |
|---|---|---|
| Mean | 5 | (2 + 3 + 3 + 8 + 9) ÷ 5 |
| Median | 3 | middle value of the sorted set |
| Mode | 3 | the value that repeats most |
When the mean misleads and the median is better
The mean is sensitive to outliers: a single very large or very small value drags it. Think of five salaries of 20, 22, 24, 26 and 200 (in thousands): the mean is 58.4, a figure no employee actually earns because the 200 inflates it. The median, however, is 24 and describes the typical group far better. That is why incomes, house prices and waiting times are almost always reported with the median instead of the mean.
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Preguntas frecuentes
- What is the difference between mean, median and mode?
- The mean is the arithmetic average (sum divided by count), the median is the middle value of the sorted data, and the mode is the most frequently occurring value. They can all be different for the same data set: for 2, 2, 3, 10 the mean is 4.25, the median is 2.5 and the mode is 2.
- When should I use the median instead of the mean?
- Use the median when your data has outliers or is skewed, because a few very large or very small values pull the mean toward them but barely move the median. Incomes, house prices and response times are usually reported with the median, since a handful of extreme values would distort the average.
- What happens if there is more than one mode?
- A data set can have several modes when two or more values tie for the highest frequency. Such data is called bimodal (two modes) or multimodal (more than two). This calculator lists every value that shares the top frequency, separated by commas.
- What if no number repeats?
- If every value appears exactly once, there is no mode at all, and the calculator shows "No mode". The mean, median and range are still computed normally, since they do not depend on repetition.
- How is the median found when there is an even number of values?
- With an even count there is no single middle value, so the median is the average of the two central numbers of the sorted list. For 3, 5, 8, 10 the two central values are 5 and 8, so the median is 6.5.