Richard Pogge

Statistics [Raw (Percent out of 50)]:

• Mean: 34.09 (68.18%)
• Spread: 7.96 (15.92%)
• Median: 35 (70%)

What do each of these numbers mean?

• The Mean of the curve is the average (the "arithmetic mean") of the all of the exam scores. It is computed by adding up the scores for all of the students and dividing by the number of students.
• The Spread in the curve is a measurement of the distribution of scores above and below the mean. In simple terms, it is the characteristic width of the grade curve, defined mathematically as the "standard deviation" of the scores. A large spread in a grade curve means that the scores were spread over a large range, making the curve wide and shallow. A large "tail" of low scores will also result in a larger spread in scores. A tall, narrow curve (small spread) means most people scored pretty close to the mean grade.
• The Median is the score that divides the grade curve down the middle (think about the so-called "median-line" in the road: the line painted down the middle). Half of the students score at or above the median, and the other half at or below the mean. The median is another way of judging the class performance, since the arithmetic mean can be skewed slightly by having a number of very high or very low scores. If the curve has a long tail towards lower scores, as it the case here, then the median is a better measure of class performance than the mean. If the curve is a symmetric bell curve, the mean and median are the same.

In this example, the grade distribution curve is slightly lopsided towards low scores. This is why the median (35) is larger than the mean (34.09) by a little bit. The more lopsided a curve is (on either side), the greater the difference between the median and mean.