Both the mean and the median are ways of measuring the center of a distribution. They tell us slightly different things, however.

The dot plot shows the number of stickers on 30 pages. The mean number of stickers is 21 (marked with a triangle). The median number of stickers is 20.5 (marked with a diamond).

<p>A dot plot for stickers on a page. The numbers 8 through 34, in increments of 2, are indicated. A diamond is indicated at 20.5 stickers and a triangle is indicated at 21 stickers. Data are as follows: 9 stickers, 1 dot; 10 stickers, 1 dot; 11 stickers, 2 dots; 12 stickers, 1 dot; 14 stickers, 1 dot; 16 stickers, 2 dots; 17 stickers, 1 dot; 18 stickers, 2 dots; 19 stickers, 1 dot; 20 stickers, 3 dots; 21 stickers, 1 dot; 22 stickers, 3 dots; 23 stickers, 1 dot; 24 stickers, 2 dots; 26 stickers, 2 dots; 28 stickers, 1 dot; 30 stickers, 1 dot; 32 stickers, 2 dots; 33 stickers, 1 dot; 34 stickers, 1 dot.</p>  

The mean tells us that if the number of stickers were distributed so that each page has the same number, then each page would have 21. We could also think of 21 stickers as a balance point for the number of stickers on all of the pages in the set. 

The median tells us that half of the pages have more than 20.5 stickers and half have less than 20.5 stickers. In this case, both the mean and the median could describe a typical number of stickers on a page because they are fairly close to each other and to most of the data points.

Here is a different set of 30 pages with stickers. It has the same mean as the first set, but the median is 23 stickers.

<p>A dot plot for “stickers on a page.” The numbers 8 through 34, in increments of 2, are indicated. A triangle is indicated at 21 stickers, and a diamond is indicated at 23 stickers. The data are as follows: 9 stickers, 1 dot; 10 stickers, 1 dot; 13 stickers, 1 dot; 14 stickers, 1 dot; 16 stickers, 1 dot; 17 stickers, 1 dot; 19 stickers, 1 dot; 20 stickers, 2 dots; 21 stickers, 2 dots; 22 stickers, 3 dots; 23 stickers, 6 dots; 24 stickers, 5 dots; 25 stickers, 4 dots; 26 stickers, 1 dot.</p>  

In this case, the median is closer to where most of the data points are clustered and is therefore a better measure of center for this distribution. That is, it is a better description of the typical number of stickers on a page. The mean number of stickers is influenced (in this case, pulled down) by a handful of pages with very few stickers, so it is farther away from most data points.

In general, when a distribution is symmetrical or approximately symmetrical, the mean and median values are close. But when a distribution is not roughly symmetrical, the two values tend to be farther apart.