Mean, Median, and Mode

Mean

When referring to the mean, many people use the ordinary English term “average.” In statistics we use the more precise term “arithmetic mean” or “samplemean.” In statistics, the term “average” can also refer to other statisical measures.

The mean is often used to represent a set of data collected in an investigation. In air quality work we calculate the mean in a variety of situations.

For a data set, the mean is the sum of all the observations divided by the number of observations.

Median

Whenever you find yourself saying, "the average worker" or "the average household," you may want to use the median to describe those situations. You want a statistic that tells you something about the worker or the household in the middle.

The median literally is the value in the middle. Just line up the values in your set of data, from largest to smallest—the one in the center is your median. If there are two values in the middle, calculate the mean of the two values.

Here's an illustration highlighting the difference between the mean and the median:

  • Ten people are riding on a bus in Redmond, Washington. The mean income of those riders is $50,000 a year. The median income of those riders is also $50,000 a year.
  • George Begaye, who gets $50,000 a year, gets off the bus. Bill Gates gets on.
  • The median income of those riders remains $50,000 a year. But the mean income is now somewhere in the neighborhood of $50 million. Someone might say that the average (mean) income of those bus riders is 50 million bucks. But those other nine riders didn't become millionaires just because Bill Gates got on their bus.
  • Reporting that the "average rider" on that bus earns $50,000 a year, using the median, provides a far more accurate picture of those bus riders' place in the economy.

Mode

The mode of a data set is the value that occurs most often.

For example, in the data set 1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17 the mode is 6.

A data set might have two values that occur most often.

For example, in the data set 1, 3, 3, 3, 3, 5, 6, 6, 7, 7, 7, 7, 9, 12, 15, 17, 17 there are two modes: 3 and 7. This situation is called a “bimodal” distribution.

Note: The term “average” can be correctly used to indicate mean, median, or mode.

For more information on statistics visit the following websites.

(links Median and Mode at page bottom)

Revised 2/9/11 pe