Definitions of Average: Mean, Median and Mode

THE MOST COMMON DEFINITIONS OF ’AVERAGE’

These definitions refer to this set of numbers: 5, 5, 5, 8, 12, 14, 21, 33, 38.

Mean (arithmetic mean)

The mean is the most commonly used type of average. It is total of all the numbers divided by the how many numbers there are. In this case there are 9 numbers with a total of 5+5+5+8+12+14+21+33+38 = 141. The mean is therefore 141 divided by 9, or 15.6444 (rounded to 15.6).

Median

For an odd number of numbers, the median is the middle number when they are arranged in order. The above set has 9 numbers, and they are in order: the middle number, i.e. the median, is 12. (For an even number of numbers the median is mid-way between the two middle numbers. So if we had just 8 numbers, 5, 5, 5, 8, 12, 14, 21, 33, the median would be mid-way between 8 and 12, i.e. 10.)

Mode

The mode is the number that occurs most frequently in a data set. For this set, the number 5 occurs most often, so the mode is 5. (If two or more numbers occur jointly most often the data set is bi-modal or multi-modal. In this case the mode may be of limited usefulness.)