📊 Average Calculator
Paste or type a list of numbers to find the mean, median, mode, range, sum and count in one go.
Quick answer: The average (mean) is the sum divided by the count: for 4, 8, 15, 16, 23 and 42 the sum is 108, so the mean is 108 ÷ 6 = 18. The median of the same list is 15.5 and the range is 38.
Updated · Free · No sign-up · Works on any device
Average Calculator inputs
Result
Mean (average)
18
108 ÷ 6 = 18
- Median
- 15.5
- Mode
- No mode
- Range
- 38
- Count
- 6
- Sum
- 108
| Minimum | 4 |
| Maximum | 42 |
| Sorted values | 4, 8, 15, 16, 23, 42 |
Step by step
- Sum: 4 + 8 + 15 + 16 + 23 + 42 = 108
- Mean: 108 ÷ 6 = 18
- Median: average of the two middle values (15 + 16) ÷ 2 = 15.5
- Mode: every value appears once, so there is no mode
- Range: 42 − 4 = 38
Three kinds of average
“Average” usually means the arithmetic mean, but the median and mode are averages too – each describes the centre of a data set in a different way.
Mean = (x₁ + x₂ + … + xₙ) ÷ n · Range = Maximum − Minimum
- Mean: add all values, divide by how many there are.
- Median: sort the values; take the middle one, or the average of the two middle ones if the count is even.
- Mode: the most frequent value. A list can have one, several or no mode.
- Range: the spread between the largest and smallest values.
Worked example
Take the list 4, 8, 15, 16, 23, 42.
| Statistic | Working | Result |
|---|---|---|
| Sum | 4 + 8 + 15 + 16 + 23 + 42 | 108 |
| Mean | 108 ÷ 6 | 18 |
| Median | (15 + 16) ÷ 2 | 15.5 |
| Mode | every value appears once | none |
| Range | 42 − 4 | 38 |
Notice the mean (18) is pulled above the median (15.5) by the single large value 42 – a sign of right-skewed data.
Choosing the right average
The mean uses every value, which makes it the best summary for roughly symmetric data such as test scores or heights. The median resists outliers, so it is preferred for incomes, house prices and response times. The mode is the only average that works for categories, such as the most common shoe size sold.
Tips for entering data
- Separate numbers with commas, spaces, semicolons or line breaks – you can paste a column straight from a spreadsheet.
- Don’t use commas as thousands separators (write 12000, not 12,000), because commas split values.
- Negative numbers and decimals are fine; up to 10,000 values are supported.
Frequently asked questions
What is the difference between mean, median and mode?
The mean adds every value and divides by how many there are. The median is the middle value once the list is sorted. The mode is the value that appears most often. They coincide for symmetric data but can differ a lot when the data is skewed.
How do you find the median of an even number of values?
Sort the values and take the average of the two in the middle. For 3, 5, 8, 10 the middle pair is 5 and 8, so the median is 6.5.
Can a list have more than one mode or no mode?
Yes. If two or more values share the highest frequency the data is bimodal or multimodal, and all of them are modes. If every value appears exactly once there is no mode.
When should I use the median instead of the mean?
Use the median when a few extreme values would distort the mean – house prices and incomes are classic examples. One billionaire moves the mean income of a town enormously but barely changes the median.