Median

Defining the Median

In statistics the median refers to the “middle number” in a set of participants’ data scores or observations. [Page 973]The median is the number separating the higher half of the scores from the lower half. The median value is calculated in two ways, depending on whether the number of scores is even or odd. If there is an odd number of scores, the median value can be found by arranging all the participants’ scores in order from lowest value to highest value and then selecting the middle score. For example, suppose a researcher conducted a study on the number of times adolescents had talked to their parents about sexual safety and the following 11 scores were reported: 2, 4, 1, 3, 45, 8, 0, 4, 5, 7, and 2. To calculate the median, the researcher would arrange the scores in order from lowest to highest:

$$01223\left\{4\right\}457845.$$

Then, since there is an odd number, the researcher would select the middle score, 4, as the median because half the scores are above and half the scores are below 4.

However, if there is an even number of scores, the median must be found by arranging all the participants’ scores in order from lowest value to high values, similar to the first method. Since there is no single middle score, however, the median is then calculated as the average of the two middle scores. For example, suppose that in the study on the number of times adolescents had talked to their parents about sexual safety, there were 12 scores reported: 2, 4, 1, 3, 45, 8, 0, 4, 5, 7, 2, and 1. To calculate the median, the researcher would still arrange the scores in order from lowest to highest:

$$01122\left\{34\right\}457845.$$

Since there is an even numbers of scores, once they are arranged in order, and numbers 3 and 4 are in the middle, the researcher would add the two middle numbers (i.e., 3 + 4 = 7) and then divide the total by two (i.e., 7 / 2 = 3.5) to compute a median of 3.5 for the data.

Median Notations and Statistical Formula

In terms of statistical notation, researchers represent median as Mdn, or sometimes as μ½ or M. Since there is no widely accepted standard for the median notation, it is important for researchers to be explicit when introducing the symbol for median so as not to confuse it with other notations. Although researchers can calculate the median in a simple descriptive way, as previously demonstrated, researchers in communication often collect much larger sample sizes and a statistical formula or using computer software (e.g., SPSS, SAS, Stata, Mplus, R) may be more efficient. The Mdn is expressed as

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