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Mean, Median & Mode Calculator

Calculate the mean, median and mode online — free and step by step. Enter a list of numbers and get the average, the middle value and the most frequent value.

Quick answer
How do you calculate the mean?
Add all the numbers and divide by how many there are. Example: 4, 8, 15, 16, 23, 42 — the sum is 108, divided by 6 gives a mean of 18. The median is the middle value of the ordered list (here (15 + 16)/2 = 15.5), and the mode is the value that occurs most often.
The tool

Enter values — get full working

Which average? — the arithmetic mean
Comma or dot as decimal separator, negative values allowed.
Step-by-step
Press Calculate to see every step.
HowTo

Calculate the mean — 4 steps

Worked through the list “4, 8, 15, 16, 23, 42”
  1. 1
    Step 1 of 4

    Collect all the values

    Write down the numbers and count them: 4, 8, 15, 16, 23, 42 — that’s 6 values.

  2. 2
    Step 2 of 4

    Add the values

    4 + 8 + 15 + 16 + 23 + 42 = 108. That’s the sum of all values.

  3. 3
    Step 3 of 4

    Divide by the count

    108 ÷ 6 = 18. The arithmetic mean is 18.

  4. 4
    Step 4 of 4

    Sense-check the result

    The mean 18 sits between the smallest (4) and largest value (42) — plausible. For median and mode, switch the mode above.

Examples

Mean, median, mode — worked examples

Three measures of centre for the same data
Mean of 4, 8, 15, 16, 23, 42
sum = 108
108 ÷ 6
18
Mean of 5, 10, 15
sum = 30
30 ÷ 3
10
Median of 4, 8, 15, 16, 23, 42
ordered
(15 + 16)/2
15.5
Median of 3, 7, 9
ordered
middle value
7
Mode of 2, 4, 4, 5, 7, 4, 9
4 occurs 3×
4
Mean of 1, 2, 3, 4
sum = 10
10 ÷ 4
2.5
Theory

Mean, median and mode — the three measures of centre

A measure of centre sums up a data set in a single typical number. The arithmetic mean (the everyday “average”) is the sum of all values divided by their count. It uses every value but is sensitive to outliers: one very large value pulls the mean upward. The median is the value in the middle of the list once it is ordered by size — for an even count, the average of the two middle values. It is robust against outliers and often describes “the middle” more realistically, for instance with incomes. The mode is the most frequently occurring value; it is the only measure of centre that also makes sense for non-numeric data (e.g. favourite colours). A data set can have no mode, one mode, or several. Mean, median and mode belong to descriptive statistics from grade 7–8 onward and are the foundation for data analysis and charts.

Pitfalls

Common mistakes with measures of centre

Not ordering before the median

The median is the middle value of the sorted list. Unordered, you read off the wrong number.

Taking one value for an even count

With 6 values there are two middle ones — the median is their average, not either one.

Ignoring outliers

A single extreme value shifts the mean a lot. The median is often more informative then.

Confusing mode with mean

The mode is the most frequent value, not the average. The two can be far apart.
FAQ

Frequently asked questions about mean, median and mode

Glossary

Glossary — key terms explained simply

Arithmetic mean
The sum of all values divided by their count.
Median
The middle value of the list ordered by size.
Mode
The most frequently occurring value.
Measure of centre
A figure that summarises a data set in one typical value.
Outlier
A single value that differs greatly from the rest.
Bimodal
A data set with two values tied as most frequent.