How to use the calculator
Type or paste your numbers into the box and press Calculate. Numbers can be separated by commas, spaces, tabs or new lines, so you can paste a column straight from a spreadsheet. Decimals and negative numbers are fine. Do not use thousands separators, because a comma is read as the start of a new number. Up to 10,000 numbers are accepted.
If an entry is not a number, the calculator lists the first few problem entries so you can fix them.
What each result means
- Mean is the ordinary average: the sum of all values divided by how many there are.
- Median is the middle value after sorting. With an even count it is the average of the two middle values.
- Mode is the value that appears most often. There can be more than one mode. If every value appears only once, there is no mode.
- Range is the largest value minus the smallest.
- Standard deviation describes how spread out the values are around the mean.
Worked example
Take the list 3, 7, 7, 2, 9, 4.
- Count: 6 and sum: 32, so the mean is 32 / 6 ≈ 5.33.
- Sorted: 2, 3, 4, 7, 7, 9. The two middle values are 4 and 7, so the median is 5.5.
- 7 appears twice and every other value once, so the mode is 7.
- The range is 9 − 2 = 7.
Standard deviation
Subtract the mean from each value, square the differences and add them up. Divide that total by n for the population standard deviation, or by n − 1 for the sample standard deviation, then take the square root. Use the population version when your list contains every member of the group you care about, and the sample version when the list is a sample drawn from a larger group.
Good to know
- The mean is pulled toward extreme values, while the median is not. For skewed data such as incomes or house prices, the median often describes a typical value better.
- The sample standard deviation needs at least two numbers.
- Results are rounded to at most 10 decimal places for display.