Definition: median from Philip's Encyclopedia

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.

Summary Article: Median
from Encyclopedia of Survey Research Methods

Median is a descriptive statistic that researchers commonly use to characterize the data from their studies. Along with the mean (average) and mode, the median constitutes one of the measures of central tendency—a general term for a set of values or measurements located at or near the “middle” of the data set. The median is calculated by sorting the data set from the lowest to highest value and taking the numeric value occurring in the middle of the set of observations. For example, in a data set containing the values 1, 2, 3, 4, 5, 6, 7, 8, and 9, the median would be the value 5 as it is the value within the data set that appears in the middle—with four observations less than and four observations greater than the median value. The median can also be thought of as the 50th percentile.

It is possible that a data set can have a median that is not a specific observation within the data set. This happens when the data set has an even number of observations. In this instance, the median would be the mean of the two middle numbers. For example, in a data set containing the values 1, 2, 3, 4, 5, and 6, the median would fall between the values 3 and 4. In this instance, the median would be 3.5. There are three observations less than and three observations greater than the median value.

Unlike the mean, the median is not influenced by extreme outlying data points within the data set. For instance, in a response to a survey question about annual personal income, if one respondent reports an income that is 10 times greater than the next closest person, this respondent would be an outlier and would skew the mean value upward. However, the median would be unaffected by this outlier and would more accurately represent the middle of the data set. Thus, the median is often used when a data set has outlying data points that could influence the mean and thereby misrepresent the middle of the data set. This also is common in survey questions on home prices or issues related to costs and finances, when extreme outliers can dramatically affect the mean value. In this instance, presenting the median value would be much more informative about the average value of housing than the mean, as the median is not influenced by the outlying values.

• Mean; Mode; Outliers; Percentile

• (1999). Math dictionary with solutions: A math review. Thousand Oaks, CA: Sage.

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