About the Mean, Median, Mode Calculator
This mean, median, mode calculator gives you all the measures of central tendency for a data set in one go. Paste or type your numbers separated by commas, spaces or new lines — straight from a spreadsheet column works — and you get the mean (average), the median (middle value), the mode (most frequent value) and the range (largest minus smallest).
It is made for students doing statistics homework, teachers checking answers, and anyone summarising test scores, prices, times or survey responses. The sorted list and frequency chart make it easy to see how the median was found and why a particular value is the mode.
When every value appears only once there is no mode, and when two or more values tie for the highest count the data set is bimodal or multimodal — the calculator lists all of them. Anything that is not a number is ignored.
With the default inputs, the mean (average) is 15.4444. Change any value above to recalculate instantly.
How to use the mean, median, mode calculator
- 1Paste or type your numbers, separated by commas, spaces or line breaks.
- 2Read the mean, median, mode and range at the top of the results.
- 3Check the sorted list to see which value sits in the middle.
- 4Use the frequency chart to spot the mode and any clusters or outliers.
Formula and method
The mean adds every value and divides by how many there are. The median sorts the values and takes the middle one; with an even count it averages the two middle values, which makes it resistant to outliers. The mode is the value (or values) that occur most often — a set can have no mode, one mode, or several.
The range is the simplest measure of spread: the largest value minus the smallest. Because it depends only on the two extremes, pair it with a standard deviation or interquartile range when outliers are present.
- Σx
- Sum of all values
- n
- Number of values
- max, min
- Largest and smallest values
Worked examples
Mixed list with a repeated value
The nine values add to 139, so the mean is 139 ÷ 9 ≈ 15.44. Sorted (4, 8, 8, 8, 15, 15, 16, 23, 42), the fifth value is 15, which is the median. 8 appears three times, so it is the mode, and the range is 42 − 4 = 38.
Even number of test scores
Sorted: 66, 72, 78, 85, 85, 90. With six scores the median is the average of the 3rd and 4th, (78 + 85) ÷ 2 = 81.5. The mean is 476 ÷ 6 ≈ 79.33, and 85 is the only repeated score.
No mode
All five values are different, so there is no mode. The mean is 25 ÷ 5 = 5 and the middle sorted value (1, 3, 5, 7, 9) is also 5.
Frequently asked questions
What is the difference between mean, median and mode?+
The mean is the arithmetic average, the median is the middle value when the data is sorted, and the mode is the value that appears most often. They coincide for symmetric data but can differ a lot when data is skewed.
How do you find the median with an even number of values?+
Sort the values and average the two in the middle. For 2, 4, 6, 8 the middle pair is 4 and 6, so the median is 5.
Can a data set have more than one mode?+
Yes. If two values tie for the highest frequency the set is bimodal, and with more it is multimodal. If every value appears exactly once, the set has no mode.
When should I use the median instead of the mean?+
Use the median when the data has outliers or is skewed — house prices and incomes are classic examples — because a few very large values pull the mean up but barely move the median.
How do you calculate the range?+
Subtract the smallest value from the largest. For 4, 8, 15, 16, 23, 42 the range is 42 − 4 = 38. It is quick but sensitive to a single extreme value.