The Average (Mean, Median And Mode) Calculator

The formula this calculator uses

mean = sum / count

sum

Total of all the values in the list

n

How many values the list contains

mean

Sum divided by count, the arithmetic average

median

Middle value once the list is sorted

mode

The most frequently occurring value

How to check the result by hand

1. 1

   Count the values

   The count is the denominator of the mean and it decides whether the median is a single value or the average of two. For the list 4, 8, 15, 16, 23 and 42 the count is 6.

2. 2

   Add them all up

   Summing gives 108 for that list. Include every value, including any zeros, because a zero is a real observation rather than a missing entry.

3. 3

   Divide the sum by the count for the mean

   108 divided by 6 is 18. This is the arithmetic average and it uses every value, so one extreme entry moves it.

4. 4

   Sort the list for the median

   Ordered, the list is 4, 8, 15, 16, 23 and 42. With six values there is no single middle entry, so take the third and fourth values, 15 and 16, and average them to get 15.5.

5. 5

   Tally the values for the mode

   Count how often each value appears. If one appears more than all the others it is the mode; if several tie, report all of them; if every value is unique, say there is no mode rather than picking one arbitrarily.