749. The median is.
a. the middle score when the data are arranged from highest to lowest.
b. the arithmetic average.
c. the most frequent value obtained.
d. never more useful than the mean.
A. Use your memory device: the median is the exact �middle of the highway��it is the �middle score.� In studies measuring variables with extreme scores (e.g., family size or income), the median would be the best statistic. Your exam could specify a distribution of scores and ask you to name the median score. Say, for example, your exam provides these scores: 1, 90, 12, 90, 6, 8, 7. First rank the scores from the lowest to the highest: 1, 6, 7, 8, 12, 90, 90. In this case, the median score is 8 since there are three scores above 8 (12, 90, 90) and three scores below it (1, 6, 7). Now let�s assume that the test construction committee isn�t so kind. In fact, maybe they are feeling a little sadistic that day. This time they add another score so there are eight scores rather than seven in the distribution. Now the distribution has an even rather than an odd number of scores. Assume the score of 10 was added. Thus when you rank order the distribution, it now looks like this: 1, 6, 7, 8, 10, 12, 90, 90. Do I hear some head-scratching here�maybe even a tinge of panic? What�s that you say? You can�t find a value that has an equal number of scores above and below it. Well you�re correct�it doesn�t exist. The trick here is to know that the median is a score or a �potential score� that divides the distribution in half. Therefore, when a distribution has an even number of scores, you take the arithmetic mean of the two middle scores and use this as the median. In this case: 8+10=18 and 18/2=9. The median of 9 lies midway between the middle scores of 8 and 10. In some cases, your computation could legitimately yield a fraction (e.g., 91/2).