Mean, median, mode calculator
Three different answers to "what is typical?". Drag an outlier and watch the mean chase it while the median barely moves.
- Mean = sum ÷ count = 1495 ÷ 20 = 74.75
- Median: sorted, the middle two values (positions 10 and 11), averaged = 73.5
- Mode: no value repeats, so there is no mode
- Range = max − min = 95 − 58 = 37
Sorted: 58, 60, 62, 65, 67, 69, 70, 71, 72, 73, 74, 76, 77, 79, 81, 83, 84, 88, 91, 95
Three kinds of "average"
- Mean: add everything and divide by the count. It is the balance point of the data: if the dots were weights on a ruler, the ruler would balance at the mean.
- Median: the middle value once the data are sorted. Half the values lie below it and half above.
- Mode: the most common value. The only average that works for categories, like the most popular shoe size.
Try the outlier switch
Tick "Add an outlier" and drag it far to the right. The mean slides towards it, because every value pulls on the balance point in proportion to its distance. The median shifts by at most half a position. This is why the US Census Bureau reports median household income: a handful of billionaires would drag the mean far above what a typical household earns.
Which one to use
For roughly symmetric data without outliers, the mean and median are close and the mean is the usual choice. For skewed data (right-skewed like incomes, wait times or house prices), report the median. If the mean is well above the median, the data are probably skewed right; see it in the histogram maker.
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Questions students ask
How do you find the median?
Sort the values. With an odd count, the median is the middle value. With an even count, it is the average of the two middle values.
What if there is no mode?
If every value appears exactly once there is no mode. If two or more values tie for most frequent, the data are bimodal or multimodal and all of them are modes.
When should I use the median instead of the mean?
When the data are skewed or have outliers, such as incomes or house prices. The median depends only on the middle, so a few extreme values cannot drag it.
What is the range?
The largest value minus the smallest. It is quick but depends entirely on the two most extreme values, so the interquartile range is usually a better measure of spread.