Formula
mean = (x₁ + x₂ + … + xₙ) ÷ nmedian = middle value of the sorted list (average of the two middle values if n is even)
- mode — the most frequent value(s)
- range = largest − smallest
Add everything up and divide by how many numbers there are.
Worked example
Five test scores
- Numbers
- 12, 15, 15, 18, 20
Average (mean)
16
Count: 5
Sum: 80
Median: 15
How it works
The mean adds the numbers and divides by the count. The median is the middle number once sorted, which makes it less sensitive to unusually large or small values. The mode is the value that appears most often; if every value is different there is no mode.
Decimal values are summed exactly, so 0.1 + 0.2 + 0.3 gives 0.6 rather than 0.6000000000000001. If some values should count for more than others, use Weighted Average Calculator. For exam marks across subjects see Marks Percentage Calculator.
Assumptions and limits
- Thousands separators aren't accepted inside the list (they would be read as list separators).
Related tools
Weighted Average CalculatorAverage values that count for different amounts, such as graded assignments.Percentage Difference CalculatorHow different two values are, as a percentage of their average — order doesn't matter.Marks Percentage CalculatorStudentPercentage from marks obtained, marks from a percentage, or an overall percentage across subjects.Probability CalculatorSingle events, two events (independent or exclusive) and repeated trials (binomial).Ratio CalculatorSimplify a ratio to lowest terms, or split an amount in a given ratio.Standard Deviation CalculatorStandard deviation and variance of a list of numbers, sample or population, with the working.