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# CENTRAL TENDENCY: THE MEDIAN

The median is the point in a distribution above and below which there are an equal number of scores in a distribution. If you’ve ever taken a standardized test like the ACT, SAT, or GRE and scored in 86th percentile, then 14% of the scores were higher than yours (.86 + .14 = 1.0).

Ten percent of scores in a list are below the 10th percentile and 90% are above it. The 25th percentile is called the first quartile and the 75th percentile is the third quartile. The difference between the values for the 25th and 75th percentiles is known as the interquartile range and is a measure of dispersion for ordinal and interval-level variables. (More on measures of dispersion later.)

The median is the 50th percentile. It can be used with ranked or ordinal data and with interval- or ratio-level data. For an odd number of unique observations on a variable, the median score is (n + 1)/2, where n is the number of cases in a distribution and the scores are arranged in order.

Suppose we ask nine people to tell us how many brothers and sisters they have, and we get the following answers:

0 0 1 1 1 1 2 2 3

The median observation is 1 because it is the middle score—there are four scores on either side of it, (n + 1)/2 = 5, and we see that the median is the fifth case in the series, once the data are arranged in order.

Often as not, of course, as with the data on those 30 respondents from the green survey shown in table 20.2, you’ll have an even number of cases. Then the median is the average of n/2 and (n/2 + 1), or the midpoint between the two middle observations, once the data are arranged in order. I asked 16 undergraduate students ‘‘How long do you think you’ll live?’’ Here are the responses:

70 73 75 75 79 80 80 83 85 86 86 87 87 90 95 96

n/2 = 8 and n/2 + 1 = 9, so the median is 84, midway between the two middle observations, 83 and 85. (By the way, if the two middle observations had been, say, 83, then the midpoint between them would be 83.)

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