Average Calculator: Mean, Median, Mode and Range
The mean is the sum divided by the count. For 2, 4, 4, 4, 5, 5, 7, 9 the sum is 40 and there are 8 values, so the mean is 5. The median (middle value) is 4.5, the mode (most common) is 4 and the range is 9 − 2 = 7.
Separate values with commas, spaces or new lines. You can paste a column from a spreadsheet.
Mean (average)
5
Median
4.5
Mode
4
Range
7
Count
8
Sum
40
Smallest
2
Largest
9
Show the math
- 1
Add up the values
2, 4, 4, 4, 5, 5, 7, 9 → sum = 40
= 40
Read the steps as text
- Add up the values. 2, 4, 4, 4, 5, 5, 7, 9 → sum = 40
- Mean = sum ÷ count. 40 ÷ 8 = 5 The mean is what most people call the average.
- Sort the values. 2, 4, 4, 4, 5, 5, 7, 9 Median and range both need the values in order.
- Median = the middle value. Values 4 and 5 are 4 and 5 → (4 + 5) ÷ 2 = 4.5 With an even count, the median is the mean of the two middle values.
- Mode = the most common value. 4 appears 3 times
- Range = largest − smallest. 9 − 2 = 7
Mean, median and mode
All three are kinds of average, each answering a slightly different question. The mean adds every value and divides by how many there are; it's what people usually mean by "the average". The median is the middle value once the list is sorted, or the mean of the two middle values when there's an even number of them. The mode is the value that appears most often.
A list can have no mode (if nothing repeats) or several (if two or more values tie for most common). The calculator shows all of them. The range, largest minus smallest, is a quick measure of how spread out the numbers are.
Which average should you use?
The mean uses every value, which makes it sensitive to outliers. If four people earn $40,000 and one earns $1,000,000, the mean income is $232,000, which describes nobody. The median, $40,000, is far more typical, which is why house prices and incomes are usually reported as medians.
The mode is most useful for categories and repeated values, like the most common shoe size sold. For evenly spread data without outliers, the mean and median come out close together.
Frequently asked questions
- How do I calculate the average of a list of numbers?
- Add all the numbers together, then divide by how many there are. The average of 3, 7 and 8 is (3 + 7 + 8) ÷ 3 = 6.
- How do I find the median of an even number of values?
- Sort the values and take the mean of the two in the middle. For 2, 4, 6, 8 the middle values are 4 and 6, so the median is 5.
- Can there be more than one mode?
- Yes. If two or more values tie for appearing most often, they are all modes. If every value appears only once, there is no mode.
- Can I paste numbers from a spreadsheet?
- Yes. Copy a column or row and paste it in. Numbers can be separated by commas, spaces, tabs or new lines.