Calculators

Average Calculator

Mean, median, mode, range and standard deviation of any list of numbers. Paste a column straight from a spreadsheet.

How it works

The mean adds every value and divides by how many there are. The median is the middle value once sorted, or the average of the two middle values. The mode is the value that appears most often. Standard deviation measures the typical distance from the mean. The sample version divides by n − 1, which corrects for a sample underestimating the spread of the whole population.

mean = Σx ÷ n | s = √(Σ(x − mean)² ÷ (n − 1))
n
How many numbers there are
Σx
Their sum
Range
Largest minus smallest
σ
Population standard deviation, dividing by n

Worked example

Seven test scores: 72, 85, 90, 66, 85, 78, 94.

  1. 1Sum: 570; count: 7; mean: 570 ÷ 7 = 81.43
  2. 2Sorted: 66, 72, 78, 85, 85, 90, 94, so the median is 85
  3. 385 appears twice, so it is the mode
  4. 4Range: 94 − 66 = 28; sample standard deviation: 9.96

Mean 81.43, median 85, mode 85. The mean sits below the median because of the low 66.

Frequently asked questions

Should I use the mean or the median?

The mean uses every value, which is ideal when the data is roughly symmetrical. The median ignores extremes, so it gives a fairer typical value when a few numbers are far off, as with incomes or house prices. When the two differ a lot, report the median.

Sample or population standard deviation?

Use sample (n − 1) when your numbers are drawn from a larger group you want to describe, which is most real data. Use population (n) only when you have every member of the group, such as the marks of every student in one class.

What if there is no mode?

If no value appears more than once, the list has no mode. If several values tie for most frequent, they are all modes, and the calculator lists each one.

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