What this calculator does
Find the average of any list of numbers, along with the median and mode. An average is one number that stands in for a whole set of values. The everyday "average" is the mean: add everything up and share it out evenly. The median (the middle value) and the mode (the most common value) are other kinds of average. They can tell a different story about the same numbers.
You also get the count, the sum, the smallest and largest values, and the range between them. The working sorts your list and shows how each figure is found. A frequency table shows how often each value appears, which makes the mode easy to check.
Where it's used
Why this math matters outside the classroom:
- Test results. A student who scored 82, 90, 75 and 93 has a mean score of 340 ÷ 4 = 85.
- House prices. Real estate reports use the median price because one $5 million house barely moves the median but pulls up the mean.
- Shoe stock. A shoe store restocks the mode, the size it sells most often, rather than the mean size.
- Weekly weather. A week with highs of 70, 72, 68, 75, 71, 69 and 72 °F has a mean high of 71 °F and a range of 7 degrees.
- Points per game. A basketball player scoring 18, 24, 15, 30 and 23 points averages 110 ÷ 5 = 22 points per game.
Grade level and standards: Grade 6; Common Core State Standards for Mathematics 6.SP.B.5.c, 6.SP.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter your numbers separated by commas, spaces or new lines. You can paste a column straight from a spreadsheet.
- Leave out thousands separators: type 1500, not 1,500. Commas are read as gaps between numbers.
- Read the mean as the main result. The median, mode and other summary values are listed below it.
- Open the working to see the sum, the sorted list, the middle value or values for the median, and the subtraction for the range.
What the inputs mean
- Numbers
- Up to 10,000 numbers. Negatives and decimals are fine. Anything that isn't a number is flagged so you can fix it.
Formula and method
mean = (x1 + x2 + ... + xn) ÷ n median = middle value of the sorted list (average of the two middle values when n is even) mode = the value or values that appear most often range = maximum − minimum
In the formulas, x1, x2 and so on are your numbers, and n is how many numbers there are. The mean adds every value and divides by n. The median sorts the values and takes the one in the middle. So it isn't thrown off by a very large or very small value at either end.
The mode is the value that appears most often. If several values tie for the most appearances, all of them are listed. If no value repeats, there's no mode.
Worked example
Six test scores: 12, 15, 15, 18, 22 and 27.
- Sum: 12 + 15 + 15 + 18 + 22 + 27 = 109.
- Mean: 109 ÷ 6 ≈ 18.1667.
- Median: the list is already sorted. With six values, the middle pair is the 3rd and 4th: 15 and 18. So the median is (15 + 18) ÷ 2 = 16.5.
- Mode: 15 appears twice, more than any other value.
- Range: 27 − 12 = 15.
Result: Mean ≈ 18.1667, median 16.5, mode 15, range 15.
Understanding the result
If the mean is clearly higher than the median, a few large values are pulling it up. If it's lower, a few small values are pulling it down. For lopsided data like incomes or house prices, the median is often the better summary.
The range shows how spread out the values are. But it depends only on the two most extreme numbers.
Assumptions and limitations
- Every number counts equally. There are no weights.
- Sums use a careful adding method (compensated summation), so long lists of decimals stay accurate.
- This is a simple mean, where every number counts the same. For a weighted average, such as grades with different credit values, multiply each value by its weight first.
- Geometric and harmonic means aren't calculated here. To measure spread beyond the range, use the standard deviation calculator.
- Thousands separators aren't supported, because commas separate the numbers.
Frequently asked questions
Which should I use: mean or median?
Use the mean when values are fairly evenly spread and you want every value to count. Use the median when a few very large or very small values would skew the picture. The median shows the typical middle value.
Can a data set have more than one mode, or none?
Yes to both. In 1, 1, 2, 2, 3, both 1 and 2 are modes. In 1, 2, 3, every value appears once, so there's no mode.
How do I find the median of an even number of values?
Sort the values and average the two in the middle. For 12, 15, 15, 18, 22, 27, the middle pair is 15 and 18, giving 16.5.
How do I work out an average by hand?
Add all the numbers, then divide by how many there are. Four quiz scores of 8, 9, 6 and 9 add to 32. And 32 ÷ 4 = 8, so the average is 8.
What score do I need on the next test to reach a target average?
Multiply the target average by the number of tests, counting the next one. Then subtract the total you already have. Say you want to average 85 over five tests, and you've scored 80, 90, 78 and 84 (332 in total). You need 85 × 5 − 332 = 93.
When should I use a weighted average instead?
Use it when the values don't count equally. Examples are course grades where a final exam is worth more than a quiz, or prices bought in different amounts. Multiply each value by its weight, add those up, and divide by the total weight. The weighted average calculator does this for you.
What is the average of a single number?
It's the number itself. The mean and median both equal that value, and the range is zero. Nothing repeats, so the calculator reports no mode.
How this calculator is checked
Method: Standard definitions of arithmetic mean, median, mode and range from descriptive statistics. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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