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Mean Median Mode Calculator

Paste a list of numbers to get all three averages at once — mean, median and mode — plus the range, midrange and a count of every value.

Your data set

Separate values with commas, spaces or new lines — order does not matter.
Sorted values
2, 4, 4, 6, 6, 6, 7, 7, 7, 7, 8
Mean working
64 ÷ 11 = 5.8182
Mean (average)
5.8182
Median
6
Mode
7
Range
6
Midrange
5
How many values
11
Sum
64
7
appears 4 times
6
appears 3 times
4
appears 2 times
2
appears 1 time
8
appears 1 time

How to use this calculator

  1. Type or paste your data set. Commas, spaces and new lines all separate values, and the order does not matter — sorting happens automatically.
  2. Read the mean at the top and the median, mode, range and midrange beside it. The sorted list under the box shows the data in the order the median was taken from.
  3. Open the working panel for a count of how often each value appears. That is the evidence behind the mode, and it is where a bimodal set becomes obvious.

How the mean, median and mode are calculated

All three are called averages, but they are three different questions about the same data.

Mean = Σx ÷ n
  • Σx — every value added together, e.g. 64
  • n — how many values there are, e.g. 11
  • Mean — the result, e.g. 5.8182

The median needs sorting rather than arithmetic. Put the values in order and take the one in position (n + 1) ÷ 2 — the sixth of eleven values here, which is 6. With an even count that position falls between two values, so the median is their average.

The mode needs counting. In the example, 7 appears four times, more than any other value, so the mode is 7. A set can have one mode, several, or none.

What each measure tells you

The question each measure answers
MeasureThe question it answers
MeanWhat would each value be if the total were shared equally?
MedianWhat is the middle value, with half above and half below?
ModeWhich value comes up most often?
RangeHow far apart are the highest and lowest?
MidrangeWhat sits halfway between the two extremes?

Reporting one average alone hides more than it shows. Salaries are quoted as medians because the mean is pulled up by a handful of very high earners; shoe sizes are stocked by mode because a shop needs the size people actually buy, not the arithmetic middle of the range.

Frequently asked questions

How do I find the mean, median and mode?

The mean is the total divided by how many values there are. The median is the middle value once they are sorted. The mode is whichever value appears most often. For 2, 7, 6, 4, 7, 7, 6, 8, 7, 4, 6 the mean is 5.8182, the median is 6 and the mode is 7.

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

Take the two middle values and average them. Sorted, 2, 4, 6, 7, 8, 9 has 6 and 7 in the middle, so the median is 6.5. With an odd count there is a single middle value and no averaging is needed.

What if two values tie for most common?

Then the set has two modes and both are listed — that is called bimodal, and it usually means the data contains two different groups. Nothing is wrong with the data set; it just has no single most common value.

What if every value appears once?

Then there is no mode at all, and the calculator says so rather than picking one arbitrarily. Mode is the only one of the three averages that can be missing, and the only one that works on non-numeric data such as colours or brand names.

When do the mean and median differ most?

When the data is skewed or contains outliers. The mean follows extreme values and the median ignores them, so a large gap between the two is itself a finding: it says the data is lopsided.

What is the midrange for?

It is the midpoint of the two extremes, ignoring everything in between. That makes it a quick summary but a fragile one — a single unusual reading moves it as far as it moves the range. It is most useful in weather data, where the daily mean temperature is often reported as the midrange of the high and low.