Median

Median

The median in this sample is 77, which represents the middle point in this group of raw scores. In a normal distribution, the mean and the median are the same. If a distribution is positively skewed, meaning that the test is very difficult, with most scores at the low end of the distribution and few very high scores, the mean is pulled to the positive end of the distribution and is higher than the median (Reynolds et al., 2008).A positively skewed distribution, such as the one depicted in Figure 11.1, signals a problem. Why are there so few high scores? What went wrong in the instructional process?

If a distribution is negatively skewed, it means the test was easy for the group, with most scores at the high end of the distribution and few very low scores. The distribution depicted in Figure 11.2 is one you might expect in a nursing class. After all, all students who are admitted to a nursing program are capable of achieving the objectives.

fig 11.2

The mean in a negatively skewed distribution is pulled toward the negative end of the distribution and is lower than the median (Reynolds et al., 2008). Therefore, the mean can give the wrong impression whenever a distribution is seriously skewed. The terms positively skewed and negatively skewed can seem counterintuitive. Remember this tip: A “positively” skewed distribution has its tail in the positive end of the distribution, while a “negatively” skewed distribution has its tail in the negative end of the distribution. A distribution that is not skewed has the same or very close values for the mean and the median; it resembles a bell and is referred to as a normal distribution or a bell curve.The mean and median in the example of Table 11.1 are close, which means there are probably not many extreme scores in the distribution and the mean is close to the median. The mean in this case can be interpreted as representing a typical score. Of course, you should review the score distribution, which is also included in the test analysis report, before you decide whether the mean actually represents a typical score. Interpretation of graphic and frequency distributions is discussed later in this chapter.