Calc Garden

Plot No. 56 · Education

Average Calculator (Mean, Median, Mode)

Paste a list of numbers and get the mean, median and mode at once. The mean is the sum divided by the count, the median is the middle value once sorted, and the mode is the value that appears most often. It also shows count, sum, minimum, maximum and range.

Inputs
Results
Mean (average)10.5
Median10.5
Mode12
Count6
Sum63
Minimum7
Maximum15
Range8

The mean is the sum over the count, the median is the middle of the sorted list, and the mode is the most frequent value. Range is the maximum minus the minimum.

The link saves your inputs so you can bookmark or share this exact result.

How the mean, median and mode are worked out

Paste a list of numbers and this returns every common summary at once. The mean is the sum of the values divided by how many there are. The median is the middle value once the list is sorted, or the average of the two middle values when the count is even. The mode is the value that occurs most often, and there is no mode when every value is unique.

Alongside those three averages it reports the count, the sum, the smallest and largest values, and the range, which is the maximum minus the minimum. Values can be separated by commas or spaces, and the sort and frequency count happen on every keystroke so the figures update live.

How to use the average calculator

  1. Type or paste your numbers into the box, separated by commas or spaces.
  2. Read the mean, median and mode at the top of the results.
  3. Check the count, sum, minimum, maximum and range below to sanity check the data.

Worked examples

A small data set

Inputs: 8, 12, 15, 9, 12, 7

Result: Mean 10.5, median 10.5, mode 12. Sorted the list is 7, 8, 9, 12, 12, 15; the two middle values 9 and 12 average to 10.5, and 12 is the only repeat.

No repeated value

Inputs: 3, 7, 10, 14

Result: Mean 8.5, median 8.5, mode none. With four unique values the median averages 7 and 10, and there is no most-frequent value.

Limitations and common mistakes

Edge cases and limitations

  • When several values tie for the most frequent, all of them are listed as modes, so the data can be multi-modal.
  • Results are shown to four decimal places; very long or very precise data sets may be rounded for display.

Common mistakes

  • Pasting text or stray symbols mixed in with the numbers; anything that is not a number is ignored, which can quietly change the count.
  • Expecting the mean and median to match. They only agree on symmetric data; a few large outliers pull the mean away from the median.

Frequently asked questions

What is the difference between mean, median and mode?

The mean is the arithmetic average: add every value and divide by how many there are. The median is the middle value once the list is sorted. The mode is the value that occurs most frequently. For 8, 12, 15, 9, 12, 7 the mean is 10.5, the median is 10.5 and the mode is 12.

How is the median found when there is an even count?

Sort the values, then take the two in the middle and average them. For the six sorted numbers 7, 8, 9, 12, 12, 15 the two middle values are 9 and 12, so the median is their average, 10.5.

What if no number repeats?

Then there is no mode and the calculator says so. The mode only exists when at least one value appears more than once. If several values tie for the highest frequency, they are all reported as modes.

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