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Mean, median and mode calculator (average with steps)

  

Every number counts once. Text and blanks are ignored.

Separate with commas, spaces or new lines.

Mean (average)

81.25

650 ÷ 8 = 81.25

Median
85
Mode
85
Range
27
Count
8

How we got this

  1. Mean: add all 8 numbers (650) and divide by 8.
  2. Sorted: 64, 72, 78, 85, 85, 85, 90, 91.
  3. Median: 8 is even, so average the two middle values: 85 and 85 give 85.
  4. Mode: 85 appears 3 times, more than any other value.

Which average to use

The mean uses every value, which makes it the right average for marks you want to total, but one outlier pulls it hard. The median ignores how extreme the ends are, which is why salaries and house prices are reported as medians. The mode is the only average that works for categories, such as the most common grade.

If your marks have different weights, a plain mean is wrong: use the credit-weighted GPA calculator or final grade calculator. Turning one mark into a percent is a job for the percentage calculator.

Sources

What this calculator does not account for

  • Outliers: the mean can mislead when a few values are extreme.
  • Weighted averages — enter repeated values for weights.

How this is calculated

Formula: Three averages

mean =Σx ÷ n; median =middle of the sorted list; mode =most frequent value

What the symbols mean

  • nHow many numbers there are.
  • ΣxTheir sum.

Good to know

  • With an even count, the median is the mean of the two middle values.
  • A list can have several modes, or none if nothing repeats.

Read the full methodologyFound an error? Contact us

Worked examples

Each example is worked out by the same code as the calculator above.

Test marks

72, 85, 85, 90, 64, 78, 85, 91: sum 650, mean 81.25. Sorted, the middle pair is 85 and 85, so the median is 85. 85 appears 3 times: the mode.

An outlier

3, 4, 5, 6, 40: mean 11.6, median 5. The median describes the typical value better.

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Questions

What is the difference between mean and median?

The mean adds everything and divides by the count. The median is the middle value once sorted, so one very large or small number barely moves it.

What if no number repeats?

Then there is no mode. If two values tie for most frequent, both are modes.

How do I find the median of an even list?

Sort it and average the two middle numbers. For 2, 4, 6, 8 that is (4 + 6) ÷ 2 = 5.