# Median

### value items average arithmetic

The median is a measure of central tendency, like an average. It is a way of describing a group of items or characteristics instead of mentioning all of them. If the items are arranged in ascending order of magnitude, the median is the value of the middle item.

If there is an odd number of items in the group, the median can be found precisely. For example, assume that 27 test scores are arranged from the lowest to the highest; the median score is the value of the 14th item. If there is an even number of items, the median has to be estimated. It is the value that lies between the value of the two middle items. For example, assume 26 scores arranged from the lowest to the highest, the median score lies between the value of the 13th and 14th items.

What is the advantage of using the median? First, it is easier to calculate than the average or the **arithmetic mean** and may be found more or less by inspection. The more important reason however for using the median is that it is not influenced by extreme values and so may be a better measure than the average or arithmetic mean.

For example, assume that we want to know the average income in a neighborhood where most of the people live below the poverty level, but there are two large houses where the occupants are millionaires. The arithmetic mean would average out all the incomes and give the erroneous impression that the neighborhood was middle class. The median would not be affected by the extreme values.

The median is very good for descriptive **statistics** since it enables us to make statements that half the observations lie above it and half below it. From the example in the previous paragraph we could say "half the people in the neighborhood had incomes below $12,850 and half had incomes above this figure." The median often represents a real value as distinct from a calculated value which does not exist. The disadvantage of the median is that it does not lend itself to further statistical manipulation like the arithmetic mean.

See also Mode.

## Resources

### Books

Gonick, Larry, and Woolcott Smith. *The Carlton Guide to Statistics.* New York: Harper Perennial, 1993.

Selma Hughes

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