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# Median

Resources

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, if 27 test scores are arranged from the lowest to the highest; the median score is the value of the fourteenth item. If there is an even number of items, the median lies between the value of the two middle items. For example, if 26 scores are arranged from the lowest to the highest, the median score lies between the value of the thirteenth and fourteenth 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, 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 that 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 that does not exist. The disadvantage of the median is that it does not lend itself to further statistical manipulation like the arithmetic mean.

## Resources

### BOOKS

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

### OTHER

Andrews University. An Introduction to Statistics, Lesson 3Averages: Mean, Mode, Median, or Midrange? <http://www.andrews.edu/~calkins/math/webtexts/stat03.htm> (October 7, 2006).

Selma Hughes

# median

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me·di·an / ˈmēdēən/ • adj. 1. denoting or relating to a value or quantity lying at the midpoint of a frequency distribution of observed values or quantities, such that there is an equal probability of falling above or below it: the median duration of this treatment was four months. ∎  denoting the middle term of a series arranged in order of magnitude, or (if there is no middle term) the average of the middle two terms. For example, the median number of the series 55, 62, 76, 85, 93 is 76.2. technical, chiefly Anat. situated in the middle, esp. of the body: the median part of the sternum.• n. 1. the median value of a range of values: acreages ranged from one to fifty-two with a median of twenty-four.2. (also median strip) the strip of land between the lanes of opposing traffic on a divided highway.3. Geom. a straight line drawn from any vertex of a triangle to the middle of the opposite side.DERIVATIVES: me·di·an·ly adv.

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# Median

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.

## Resources

### books

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

Selma Hughes

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# Median

The middle value in a group of measurements.

In statistics, the median represents the middle value in a group of measurements. It is a commonly used indicator of what measurement is typical or normal for a group. The median is joined by the mean and the mode to create a grouping called measures of central tendency. Although the mean is used more frequently than the median, the median is still an important measure of central tendency because it is not affected by the presence or a score that is extremely high or extremely low relative to the other numbers in the group.

Peavy, J. Virgil. Descriptive Statistics: Measures of Central

Tendency and Dispersion. Atlanta, GA: U.S. Dept. of Health and Human Services/Public Health Service, Centers for Disease Control, 1981.

## EXAMPLE

125-128-129-129-129-130-130-131-133

The median is 129.

# median

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median In statistics, the middle item in a group found by ranking the items from smallest to largest. In the series, 2, 3, 7, 9, 10, for example, the median is 7. With an even number of items, the mean of the two middle items is taken as the median. Thus in the series 2, 3, 7, 9, the median is 5.

# median

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median (mee-di-ăn)
1. adj. (in anatomy) situated in or denoting the plane that divides the body into right and left halves.

2. n. (in statistics) the middle observation of a series arranged in ascending order. See also mean.

# median

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median In statistics, the average as defined by the central value in a data set when the data set is ordered by value.

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# median

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median The middle number or value in a series of numbers or values.