In that case, we would say that the test scores had a standard deviation of 2. In other words, 68% of the people fell 2 points above or 2 points below the mean. In the midterm example, suppose you were told that 68% of the people who took the test has a score from 48 to 52. Instead of using the range, we use the standard deviation when we talk about the spread of scores. In this case, maybe only one person earned 75 and the next high was 56 with everyone else falling between 46 and 56, a range of 10. The problem with the range is that one extreme score can influence it very much. You might not feel to well about your grade even though it was above the average. Suppose the range were 30 points with the high being 75 and the low being 45. One way to measure the dispersion or spread of scores is with the range (subtract the low score from the high score). Were most of the grades close to the mean, or were students’ grades far above or below the mean. In particular, you are probably wondering how far above the mean you were compared to others in the class. You might be interested to know how the scores were spread above and below the average (mean). If you were to discover that it was 50, you might feel better about your performance because you were above average. What other information might you wish to know? Perhaps you would like to know the average (mean) grade on the test. Now let’s assume that the test was very difficult and the instructor didn’t expect anyone to have mastered all of the content on it. How would you feel? The first question you might ask is how many points were possible? If you were told that 85 points were possible you might not feel too well since you correctly answered about 64% of the questions.
Suppose that you have just completed your midterm for this class and you were told that you had a score of 55.
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