Average Calculator: Mean, Median & Mode
Calculate mean, median, mode, range, and quartiles with step-by-step explanations. Your work stays on this device whenever possible.
How to use Average Calculator: Mean, Median & Mode
- Paste numbers into 'Enter Dataset (comma, space, or newline separated)'.
- Choose the 'Sample Statistics (n − 1 degrees of freedom)' or 'Population Statistics (N)' radio button; this only changes variance and deviation.
- Press 'Calculate Statistics' to see mean, median, mode, range and the quartile summary.
- Scan the outlier note, which lists values outside the Tukey fences, and the geometric and harmonic means when all values are positive.
- Use 'Load Sample' for a demonstration set or 'Clear' to empty the box.
Worked example
Enter 12, 15, 14, 13, 16, 15, 48. Sorted, the median is 15 and the mode is 15. The sum 133 over 7 values gives a mean of 19, and the range is 36. Q1 is 13, Q3 is 16, so the IQR is 3 and the upper fence is 16 + 4.5 = 20.5. The value 48 is flagged as an outlier.
When to use this tool
- A teacher summarizing quiz scores and spotting the one paper that skews the class average.
- Comparing the mean and median of household incomes in a small survey to see how skewed they are.
Important limitations
Requires at least one valid number. Datasets where every number appears an equal number of times have no mode; sets with two or more highest frequencies are reported as bimodal or multimodal.
Comparing alternatives
Other options for average calculator: mean, median & mode include MathIsFun, Calculator.net, Omni Calculator.
ToolkitPoint is not affiliated with those services.
Frequently asked questions
How are the quartiles calculated?
The data is sorted and split at the median, excluding the median itself when the count is odd, and Q1 and Q3 are the medians of the lower and upper halves. Spreadsheet functions that interpolate can give slightly different quartiles.
What if no value repeats?
When no value repeats, the mode field reads 'No mode (all values appear equally)'. If several values tie for the highest count, all of them are listed and the label changes to Bimodal or Multimodal.
Why are geometric and harmonic means missing?
They exist only when every value is greater than zero. A single zero or negative number hides both, because the logarithm and reciprocal are undefined.
How is an outlier decided?
A value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged. That is a prompt to check the entry, not proof that it is wrong.
Does the sample or population setting change the mean?
No. Mean, median, mode and range come out identical either way, because they do not depend on degrees of freedom. Only the variance and standard deviation switch between dividing by n − 1 and dividing by N.