Paste a comma-separated list of numbers to get the arithmetic mean (the usual average), with the Sum / Count working, plus sum, count, median, geometric mean, largest, smallest, and range.
Formula
The average used here is the arithmetic mean — the sum of the n values divided by n:
average = (x1 + x2 + … + xn) / n
For example, 2 + 7 + 19 + 24 + 25 = 77, and 77 / 5 = 15.4.
Median is the middle value after sorting (or the average of the two middle values when n is even). Range is largest minus smallest. Geometric mean is the n-th root of the product:
gmean = (x1 × x2 × … × xn)^(1/n)
If any xi is zero or negative, geometric mean is reported as 0.
Average, median, and range each describe a different aspect of the same list. An outlier pulls the mean and the range far more than the median, so looking at all three together is more informative than the mean alone. For mode and the sorted data set, use the mean, median, mode, and range calculator.
Examples
Default list 10, 2, 38, 23, 38, 23, 21
The sum is 155 and n is 7, so the average is 22.142857142857. Sorted, the middle value is 23 (the median). Largest 38 minus smallest 2 is a range of 36. The geometric mean is 16.412764443111.
Page example 2, 7, 19, 24, 25
The five numbers add to 77, so the average is 15.4. The median is 19, the range is 23, and the geometric mean is 10.980107129288.
Negatives and zeros
For -2, 10, 0, 10, -2 the average is 3.2, the median is 0, and the
range is 12. Because the list includes zero and negatives, the geometric
mean is 0.