# Average

The average is a single number used to represent a set of numbers. Some common kinds of averages include: the arithmetic mean (usually called the mean), the median, and the mode. There are other concepts of average as well, including the geometric mean and harmonic mean that are used in other contexts, but we will focus on the more basic concepts of mean, median and mode.

Mean, median, and mode, are all colloquially referred to as "averages." More specifically, in the context of statistics, they are referred to as central tendencies. A central tendency is the central or most typical value in the data being studied.

### Mean

The mean, also referred to as the arithmetic mean, is likely the most familiar kind of average.

Example

Cheryl earned the following points on math tests:

88, 88, 43, 96, 85

To find the mean, find the total points scored:

88 + 88 + 43 + 96 + 85 = 400

Then divide the total points by the number of tests taken.

400 ÷ 5 = 80

### Median

The median is the middle number for a set of data when the data are ordered from least to greatest or greatest to least.

Example

To find the median of Cheryl's scores, arrange the points in numerical order: 43, 85, 88, 88, 96. The median is the middle number, 88.

### Mode

The mode for a set of numbers is the number or numbers that occur most often.

Example

The mode for Cheryl's test scores is 88 because it occurs twice, and each of the other scores occurs only once.

### Did you know?

The average lifespan in the United States as of 2018 was 78.9 years. In most countries, women live longer than men. In the US specifically, the average lifespan of women is 81.4 years while that of men is only 76.3 years. That's a difference of over 5 years!