Calculate the average of any list of numbers. Paste your values to get the mean, plus the median, mode, range, sum and count in one go.
The “average” usually means the mean (sum / count), but this also shows the median (middle value), mode (most frequent) and range, since each can be the figure you need.
Mean is the arithmetic average, median is the middle value when sorted, and mode is the most common value. They can differ a lot when data is skewed by outliers.
How to Calculate the Average of Numbers
To calculate an average, add all the numbers and divide by how many there are. For 4, 8, 15, 16, 23 and 42, the sum is 108 and there are 6 values, so the average is 108 ÷ 6 = 18. The median and mode come from the same list:
| Measure | For 4, 8, 15, 16, 23, 42 |
|---|---|
| Sum and count | 108 from 6 values |
| Mean (average) | 18 |
| Median | (15 + 16) ÷ 2 = 15.5 |
| Mode | None, every value appears once |
| Range | 42 − 4 = 38 |
How to Calculate the Mean, Median and Mode
Each measure follows a short rule, and the tool returns all three with the range, sum and count.
Formula: Mean = (sum of all values) ÷ (count of values), i.e. Σx ÷ n. Median = the middle value once the numbers are sorted (for an even count n, it’s the average of the two middle values: (sorted[n/2 − 1] + sorted[n/2]) ÷ 2). Mode = the value(s) that occur most often; if every value appears only once, there is no mode. Range = maximum value − minimum value.
Here is how to find the average of 5 numbers with the steps shown, using 2, 4, 4, 4, 6:
- Add them: 2 + 4 + 4 + 4 + 6 = 20.
- Divide by the count: 20 ÷ 5 = 4, the mean.
- Sort them and take the middle value: the 3rd of 5 is 4, the median.
- Find the most frequent value: 4 appears three times, so the mode is 4.
- Values: the numbers in the “Values” box, separated by commas, spaces or new lines.
- n: the count of values, the divisor for the mean.
- Σx (sum): the total of all values.
Example Scenarios
| Values entered | Mean (average) |
|---|---|
| 4, 8, 15, 16, 23, 42 | 18 |
| 10, 20, 30 | 20 |
| 5, 5, 5, 5 | 5 |
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | 5.5 |
| 100, 200 | 150 |
| 2, 4, 4, 4, 6 | 4 |
Which Average Should You Use?
Use the mean for fairly even data and the median when there are outliers. No single measure suits every data set:
- The mean works best when values are fairly even. One extreme value drags it: salaries of 30, 32, 35, 38 and 200 thousand have a mean of 67 thousand, which describes nobody.
- The median, the middle value, resists outliers. For those salaries it is 35 thousand, and the tool shows both so you can compare.
- The mode suits repeated values, such as the most common shoe size.
- The range, the gap between highest and lowest, is a rough guide to spread.
When the mean and median sit far apart, check for an outlier. It may just be a typo.
For grades or prices where some values count more, use a weighted mean: multiply each value by its weight, then divide by the total weight. The Wikipedia article on the arithmetic mean compares it with other averages.
Common questions about averages
How do you calculate the average of numbers?
Add all the values together, then divide by how many there are. For 10, 20 and 30 the sum is 60, and 60 ÷ 3 gives an average of 20.What’s the difference between mean, median, and mode?
Mean is the sum of all values divided by how many there are. Median is the middle value once everything is sorted, or the average of the two middle values for an even count. Mode is the value that appears most often.How do you find the median of an even set of numbers?
Sort the values, then average the two in the middle. With 4 numbers sorted low to high, you average the 2nd and 3rd values, so 10, 20, 30, 1000 has a median of 25.Why would the mean and median give very different results for the same dataset?
The mean is pulled toward extreme values, while the median isn’t. A dataset like 10, 20, 30, 1000 has a mean of 265 but a median of 25, because one large outlier drags the mean far above where most of the data sits.What if no values repeat, or several tie for the mode?
If every value appears exactly once, the calculator reports the mode as “none”. If values tie for the highest frequency it lists them all, showing the first three followed by “…” when more than three are tied.What format should I use to enter my numbers?
Separate your numbers with commas, spaces or new lines. You can also paste a mixed-format list copied from a spreadsheet or document straight into the box.Related Calculators
If your dataset needs more than a mean, the standard deviation calculator shows how spread out your values are, and the weighted average calculator is a better fit when some values should count more than others. For quick arithmetic on the side, the scientific calculator covers the rest. You may also find the Comma to New Line Converter useful. For a related estimate, try the CSV Delimiter Converter.