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Mean, Median, Mode Calculator

Find the mean, median and mode of any data set.

Result

13.0000
11.5000
8
6

How it is calculated

Enter numbers separated by commas, semicolons or spaces; entries that are not numbers are ignored. The mean is the sum divided by the count: mean = Σx ÷ n. The median is the middle value after sorting (for an even count, the average of the two middle values). The mode is the value or values that appear most often; if every value appears once, there is no mode and a message is shown. Results are shown to four decimals, with the count of values used. The median resists outliers, while the mean is pulled toward them, so the two together describe the shape of the data.

Worked example

The list is 4, 8, 8, 15, 20, 23, so n = 6. Mean = (4 + 8 + 8 + 15 + 20 + 23) / 6 = 78 / 6 = 13.0000. After sorting, the two middle values are 8 and 15, so the median = (8 + 15) / 2 = 11.5000. The value 8 appears twice and all others once, so the mode is 8. The mean sits above the median because the large values 20 and 23 pull it up.

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Common mistakes

  • Forgetting to sort before taking the median.
  • Using the middle value of an even-sized list instead of averaging the two middle ones.
  • Typing a decimal comma, such as 3,5, which is read as two separate numbers 3 and 5.
  • Expecting a single mode when two values tie; every tied value is listed.

About this calculator

This calculator finds the three classic measures of central tendency for a list of numbers: the mean (the sum of all values divided by their count, the arithmetic average), the median (the middle value once the data is sorted, or the average of the two middle values for an even-sized set), and the mode (the value or values that occur most often). Each describes the data's center from a different angle, and they diverge when the data is skewed or has outliers — the median, for instance, resists being pulled by a few extreme values in a way the mean cannot.

Statistics students and teachers use all three to build intuition for how a data set is shaped, data analysts use them to summarize survey results, sales figures, or test scores, and researchers use them as the first descriptive step before deeper statistical analysis. Anyone comparing a set of numbers — exam grades, salaries, prices, measurements — uses this to get a quick, honest picture of where the data is centered.

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Comments (1)

  • Editorial team

    Check the count line against the number of values you meant to enter. The list is split on spaces, commas and semicolons, and anything that is not a number is skipped silently, so a typo drops a value without warning. One trap: a decimal comma, as in 2,5, is split into 2 and 5. Use a decimal point inside the list. Which kind of data set do you usually run through it?

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