MultiConvers

Mean, Median, Mode and Range Calculator

Four classroom summaries from one pasted list: the arithmetic mean, the middle after sorting, the most common value, and the gap from smallest to largest. Read them together when a single average would hide a skew.

How to use

  1. Paste the numbers. Spaces, commas or new lines all work — quiz marks, sale prices, or wait times.
  2. Start with the mean, then look at the median. When those two sit far apart, a tail is usually dragging the average.
  3. Check mode and range next. Mode can be missing, or there can be more than one if two values tie for most frequent.
  4. Stop here for the school quartet. Variance and standard deviation are on the dedicated spread pages, not this one.

How it works

Teachers introduce mean, median, mode and range as a set because each answers a different question about the same list. The mean is the share if you pooled every value and split it evenly. The median is the value that splits the ordered list in half. The mode is whatever shows up most often. The range is only the distance between the extremes. Reporting one of them as “the typical number” is how a class average, a salary figure or a house-price headline can mislead.

The mean lies when a few extremes outweigh the crowd. Nine people earn 30 and one earns 300: the mean is 57, which nobody in the room actually takes home, while the median stays at 30. A single 100 on a test of otherwise mid-60s scores does the same thing. That is why housing sites and income reports often prefer the median — it does not move just because one mansion or one bonus landed in the sample. This calculator still prints the mean; it just sits next to the other three so you can see the pull.

Median construction is mechanical. Sort the list. If n is odd, take the centre. If n is even, average the two central values — so 1, 2, 3, 4 has median 2.5, not “2 or 3”. The page does that averaging; it does not pick the lower middle. Mode is a frequency count, not a middle. 1, 2, 2, 3 has mode 2. If every value appears once, there is no unique mode, and the page says so instead of pretending the smallest number is the mode. If two values tie for the highest frequency, both are listed.

Range is the crudest of the four: max minus min. One mistyped extra zero can explode it even when the mean and median barely move. It is still useful as a first “how wide is this?” check for a short homework list, but it is not a substitute for variance. This page does not compute variance or either standard deviation — those belong on the standard-deviation calculator (one method at a time) or the full statistics summary (both methods plus min, max and sum).

Use this tool when a worksheet asks for the four summaries together, or when you want a fast sense of centre versus spread without extra machinery. Use the statistics calculator when you also need sample and population spread from the same paste. Use the average calculator if you only want the mean.

Formula

Mean = Σx / n
Median = middle of the sorted list
Mode = most frequent value
Range = max − min

Worked examples

  • An odd-sized list

    1, 2, 3 → mean 2, median 2, range 2, no unique mode

  • A mode

    1, 2, 2, 3 → mode 2

Useful notes

  • Mean is sensitive to outliers; median is not.
  • If every value appears once, the page reports no unique mode rather than listing the whole set.
  • Range uses only the two extremes, so a single typo can dwarf the other three summaries.

FAQ

When is the median better than the mean?

When a few extreme values would pull the average. The median stays at the middle of the ordered list.

Can there be more than one mode?

Yes. If two values tie for most frequent, both are listed.

How is this different from the statistics calculator?

This page stops at the four school summaries. The statistics page also reports variance and both standard deviations.

What happens when the list has an even count?

The median is the average of the two central values after sorting. 1, 2, 3, 4 has median 2.5. Mean, mode and range do not change their definitions.

Can a mean sit outside most of the data?

Yes. That is the usual “the mean is lying” case: a long tail or a single extreme pulls the average away from where most values actually sit. Compare it with the median on the same paste.

Guides

Related tools

See all Statistics tools.