Mean in statistics
Most test analysis programs report the mean, or arithmetic average, of the raw scores on the test; in this case (Table 11.1), it is 75.4. The mean percent score is determined by dividing the mean raw score by the total number of items on the test. The mean percent score is equal to the mean raw score in this example because there are 100 items on the test.
One disadvantage of the mean is that it is sensitive to extreme scores. An extreme score, whether very high or very low, can pull the mean toward its direction. This effect is particularly problematic when there is a small group of scores (Reynolds, Livingston, & Wilson, 2008).
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For example, let’s look at the distributions in Table 11.2. Each distribution has an extreme score of 15, yet the smaller number of scores is affected more dramatically than the larger number of scores. The mean of the “A Scores” is 7.4, a score that does not even appear in the distribution, while the score of 15 has a less dramatic effect on the mean of the “B Scores,” which is 5.95. It is obvious from these examples that you must consider the effect of extreme scores when interpreting the mean on a test.
It is important to examine the relationship of the mean to the passing standard that you have set. If, for example, your passing standard is 75%, this test has an average score at the passing level. Several factors must be considered when interpreting the mean:
Were there extreme scores in the distribution?
What was the quality of teaching, on a range between effective and ineffective?
What was the students’ level of effort to achieve the outcomes, on a range between maximal and minimal?
Where did the material/objectives fit, on a range between too easy and too difficult?
How difficult were the items, on a range between too easy and too hard?
If a test has a very low mean, you should investigate whether there is a problem with one of the questions listed above. As Haladyna (1997) points out, if you intentionally give difficult tests, you should adjust your grading policy to ensure that you assign grades fairly in relation to the other courses that students take. Similar consideration should be made if your tests are consistently too easy. The ideal goal is to have a test with a mean that reflects a range of student abilities. A test should be neither too easy nor too difficult, but should reward those students who are high achievers and should identify those who have not met the course objectives. Chapter 13, “Assigning Grades,” discusses the issues surrounding grade assignment.
