The Average Calculator finds the arithmetic average of any list of numbers, along with the median and mode for a fuller picture of the data's center. Paste values separated by commas, spaces or line breaks, and the calculator returns the average, the sum, the count, and the two other classic measures of center, with every step of the arithmetic shown.
"Average" in everyday speech almost always means the arithmetic mean, the sum of all values divided by how many there are. This page leads with that calculation while also covering median and mode, since the three measures answer subtly different questions about the same list.
Calculate the average of a data set
The average, or arithmetic mean, is the sum of all values divided by the count of values.
average = Σx / nWorked example: find the average of 4, 8, 15, 16, 23, 42.
1. Add all the values. 4 + 8 + 15 + 16 + 23 + 42 = 108.
2. Divide by the count. 108 ÷ 6 = 18.
Understand why the average can be misleading
Every value pulls the average toward itself equally, which means a single very large or very small number, an outlier, can shift the average a long way from what most of the data actually looks like. This is why the average of a list with one extreme value can end up not resembling any of the typical entries closely.
Worked comparison: add an outlier of 200 to the earlier list (4, 8, 15, 16, 23, 42, 200).
1. Add the new sum. 108 + 200 = 308.
2. Divide by the new count. 308 ÷ 7 ≈ 44.
A single added value more than doubled the average, from 18 to about 44, even though six of the seven values are still clustered well below 44. This sensitivity is exactly why the median is often reported alongside, or instead of, the average for data that might contain outliers.
Find the median as an alternative average
The median is the middle value once the data is sorted, and it barely moves when an outlier is added, unlike the mean. Odd count: the median is the value at position (n + 1) / 2 in the sorted list. Even count: the median is the average of the two central values.
For the original set, 4, 8, 15, 16, 23, 42 (already sorted, n = 6), the two central values are 15 and 16, so the median is (15 + 16) / 2 = 15.5, close to the mean of 18. Adding the outlier 200 barely moves the median for a larger data set, which is why income and house-price summaries often quote the median instead of the mean.
Find the mode as a third measure
The mode is the value that appears most frequently in the data set. A set can have one mode (unimodal), several modes (multimodal), or no repeated value at all (no mode). For the example set, 4, 8, 15, 16, 23, 42, every value appears exactly once, so this particular set has no mode.
Choose the right average for the data
| Measure | Best used when | Sensitive to outliers |
|---|---|---|
| Mean (average) | Data is roughly symmetric | Yes |
| Median | Data is skewed or has outliers | No |
| Mode | Data is categorical, or a most-common value matters | No |
Reaching for the arithmetic mean by default is a common habit, but the median or mode can be more representative depending on how the data is shaped, particularly whenever a small number of extreme values are present.
Work through a second data set
Find the average, median and mode of 3, 3, 7, 9, 13. 1. Add the values and divide by the count. 3 + 3 + 7 + 9 + 13 = 35, and 35 ÷ 5 = 7. **2.
Find the median. With 5 values already sorted, the median sits at position 3: 7**.
3. Find the mode. The value 3 appears twice, more than any other value, so the mode is 3.
Here the mean and median both equal 7 exactly, a sign that this particular set is well balanced around its center, unlike the earlier example where an outlier pulled the mean noticeably away from the median.
Frequently asked questions
How do you calculate the average of a set of numbers?
Add all the numbers together, then divide by how many numbers there are: average = sum / count. For 4, 8, 15, 16, 23, 42, the average is 108 / 6 = 18.
Is average the same as mean?
Yes. "Average" in everyday language almost always refers to the arithmetic mean, the sum of the values divided by the count.
Why is the average sometimes not representative of the data?
Because every value contributes equally to the average, a single very large or very small outlier can pull it noticeably away from where most of the data actually sits.
What is the difference between average and median?
The average (mean) sums all values and divides by the count. The median is the middle value once the data is sorted. The median resists the pull of outliers far better than the average does.
How do you find the median of an even number of values?
Sort the data, then average the two values in the middle. For 4, 8, 15, 16, 23, 42, the two central values (15 and 16) average to 15.5.
What does it mean if a data set has no mode?
It means no value repeats; every entry in the list appears exactly once, so there is no single most-frequent value to report.
When should I use the median instead of the average?
Use the median when the data contains outliers or is meaningfully skewed, since it better represents a "typical" value in those cases than the average would.
Summary
The average of a data set is its sum divided by its count, giving 18 for the set 4, 8, 15, 16, 23, 42, but a single added outlier of 200 pushes that average up to about 44 even though most values stay small.
The median, 15.5 for the same original set, resists that pull far better, which is why it is often reported alongside or instead of the average, particularly for skewed data or data with extreme values.