Mean, median and mode are the three classic measures of central tendency — three different answers to “what is a typical value?” This calculator finds all three at once, plus the range, and shows the sorted data and a frequency table so you can check each answer by eye.
How to use the calculator
- Type or paste your numbers into the box, separated by commas, spaces or line breaks.
- Read the mean, median and mode on the tape. The range, minimum, maximum, count and sum are listed underneath.
- Open Show the work to see the sorted list and the position of the median, and scroll to the frequency table to see how often each value appears.
Negative numbers and decimals are fine, and results update as you type.
Formulas and rules
When n is odd, (n + 1) ÷ 2 is a whole number and points straight at the median. When n is even, it lands halfway between two positions, so the median is the average of those two values.
Worked example
A teacher records how many books ten students read over the summer: 7, 3, 9, 4, 7, 5, 8, 7, 6, 4.
- Mean: the values add to 60, and 60 ÷ 10 = 6 books.
- Sort: 3, 4, 4, 5, 6, 7, 7, 7, 8, 9.
- Median: with 10 values, the middle sits between positions 5 and 6, which hold 6 and 7. The median is (6 + 7) ÷ 2 = 6.5.
- Mode: 7 appears three times, more than any other value, so the mode is 7.
- Range: 9 − 3 = 6.
Here the three measures are close together, a sign that the data are fairly balanced around the center.
When the three measures disagree
The gap between mean and median is a quick test for skew:
| Shape of the data | Typical order | Example |
|---|---|---|
| Symmetric | mean ≈ median ≈ mode | Heights of adults of one sex |
| Skewed right (long high tail) | mode < median < mean | Household income, home prices |
| Skewed left (long low tail) | mean < median < mode | Scores on an easy test |
A few very large values drag the mean upward but barely move the median. That is why the U.S. Census Bureau reports median household income: in its national figures the mean is well above the median because of a small number of very high earners.
Picking the right summary
- Use the mean for symmetric data and whenever you need the total to matter, such as average spending per customer.
- Use the median for skewed data or data with outliers, and for ordered categories such as survey ratings.
- Use the mode for categories or discrete counts, such as the most common shoe size sold.
Most reports benefit from giving two of them. For spread as well as center, try the standard deviation calculator or the five-number summary calculator, which adds quartiles and a box plot. If you only need the arithmetic average in its several forms, the mean calculator covers geometric and harmonic means too.
Frequently asked questions
How do you find the median of an even number of values?
Sort the values and average the two in the middle. For 3, 4, 4, 5, 6, 7, 7, 7, 8, 9 the middle values are the 5th and 6th, 6 and 7, so the median is 6.5.
Can a data set have more than one mode?
Yes. If two values tie for the highest count the data are bimodal, and with more ties they are multimodal. The calculator lists every value that shares the top frequency.
What if no number repeats?
Then the data set has no mode. Some textbooks say every value is a mode in that case, but most treat it as 'no mode', which is what this calculator reports.
Which is better, the mean or the median?
The mean uses every value and works well for roughly symmetric data. The median ignores how extreme the largest and smallest values are, so it is the better summary for skewed data such as incomes or home prices.
Can the median be a number that is not in the data?
Yes, whenever the count is even and the two middle values differ. The mean is also often a value that never appears, such as an average of 2.4 children per family.