qcalculate

Mean, Median, Mode and Range Calculator

Type or paste a list of numbers to get all four averages and the range, and watch the numbers being sorted, added up and counted.

Separate numbers with commas, spaces or new lines.

Mean
5.6
Median
7
Mode
7
Range
7

Mean = 5.6, median = 7, mode: 7, range = 7.

In order: 2, 3, 7, 7, 9 (5 numbers, sum 28).

Show me how

All steps as text

    Tip: press ← and → to move between steps, or click any step.

    What they mean

    • Mean (the average): add all the numbers and divide by how many there are.
    • Median: the middle number once they are in order. With an even count, it is halfway between the two middle numbers.
    • Mode: the number that appears most often. There can be more than one mode, or none.
    • Range: the largest number minus the smallest. It shows how spread out the numbers are.

    Worked example: 3, 7, 7, 2, 9

    1. Sort: 2, 3, 7, 7, 9.
    2. Mean: 2 + 3 + 7 + 7 + 9 = 28, and 28 ÷ 5 = 5.6.
    3. Median: the middle (3rd) number is 7.
    4. Mode: 7 appears twice, more than any other number.
    5. Range: 9 − 2 = 7.

    Which average should I use?

    The mean uses every value, but one very large or very small number can pull it a long way. The median is not affected by such extremes, which is why house prices and incomes are usually given as medians. The mode is the only average that also works for things that aren’t numbers, like the most popular shoe size or favourite colour.

    To measure spread more fully than the range, use the standard deviation calculator.

    Questions

    Can there be more than one mode?

    Yes. In 1, 1, 2, 2, 3 both 1 and 2 appear twice, so there are two modes (the data is bimodal).

    What if no number repeats?

    Then there is no mode. The same goes when every number appears the same number of times, as in 6, 6, 2, 2.

    How do I find the median of an even number of values?

    Take the two middle numbers and find the number halfway between them: add them and divide by 2. For 1, 2, 3, 4 the median is (2 + 3) ÷ 2 = 2.5.

    Can the mean be a number that isn’t in the list?

    Yes. The mean of 1 and 2 is 1.5. The median can be too, when there is an even number of values.