The working
Every step, recomputed from whatever numbers are in the box above.
How it works
"Average" usually means the mean, but mean, median and mode are three different ways of summarising the same list of numbers, and each tells you something the others don't. The mean adds everything up and divides by the count. The median sorts the list and takes the middle. The mode is whichever value shows up most often. The range is simply the spread from lowest to highest.
mean = Σx ÷ n
median = middle value of the sorted list (average of the two middle values if n is even)
mode = the most frequently occurring value(s)
range = max − min
With the worked example 10, 12, 23, 23, 16, 23, 21, 16, sorting gives 10, 12, 16, 16, 21, 23, 23, 23. There are eight values, an even count, so the median is the average of the two middle values, 16 and 21, giving 18.5. The value 23 appears three times — more than any other — so it is the mode. The range is 23 − 10 = 13.
Common questions
What's the difference between mean, median and mode?
Mean is the sum divided by the count — the arithmetic average. Median is the middle value when everything is sorted, which resists being skewed by one extreme outlier the way the mean can be. Mode is simply whichever value appears most often.
What if there's no repeated value, or a tie for most frequent?
If every value appears exactly once, there's no mode — the calculator shows 'No mode' rather than picking one arbitrarily. If two or more values tie for most frequent, all of them are shown as modes.
Why might median be a better summary than mean?
For data with extreme outliers — like household incomes, where a few very high earners pull the average up — the median gives a more representative picture of a 'typical' value, since it isn't dragged by those outliers the way the mean is.