Median

Quantitative research in educational psychology typically begins with a description of the sample of [Page 653]subjects. This initial stage of analysis focuses on describing the center, shape, and spread (dispersion) of the observed data points. Various measures are available for describing the center, shape, and spread of a distribution of observed data points. In most instances, the researcher begins by describing the center point or central tendency of the distribution. Measures of central tendency (center) include the mean, median, and mode. The median is an often-used measure of central tendency because of the desirable characteristics it possesses.

The median is technically defined as the data point that splits the distribution of data in equal halves. That is, half of the data points fall above the median and half of the data points fall below the median. For example, suppose a mathematics assessment is administered to a group of students and the median score is found to be 74. This indicates that 50% of the students scored better than 74 and 50% scored worse than 74. Thus, the median for a data set is equivalent to the 50th percentile.

Calculating the median is rather straightforward, particularly with a small number of observed data points. When done by hand, the median can be calculated by arranging a set of observed data points in ascending (or descending) order. For example, consider seven hypothetical scores on the aforementioned mathematics assessment:

To calculate the median, the scores are first rearranged in ascending order,

and the middle score is identified. In this case, half of the scores fall above a score of 74 and half fall below a score of 74.

In a distribution consisting of an even number of observed data points, there is no “true” median. Rather, the median is calculated as the average of the middle two scores. Reconsidering the previous example with an additional observation

the centermost values are 74 and 76, which, when averaged, result in a median value of 75 (150/2).

A particularly desirable characteristic of the median is that it is unaffected by extreme or outlying data points. Unlike the mean, the median does not take into account the value of each data point in its calculation. Thus, the median often provides a more accurate representation of the center of a distribution of data points. To illustrate why this is so, reconsider the following data representing mathematics assessment scores for eight students:

This data set is fairly evenly distributed except for the lowest score of 33. This data point is 41 points lower than the median value of 74 and 33 points lower than the next smallest value of 66. When calculating the average or mean score, all of these data points are taken into consideration. The mean of the data set with the extreme observation is 69.75, whereas the mean without the extreme observation is75. On the other hand, the median score without the extreme observation does not change drastically. Whereas the median for the data set with the extreme observation is 75, the median without the extreme observation increases slightly to 76.

...