Educational Psychology / Unit 12 EDP 1143 worked example, 60 to 90 seconds
Describing a Set of Scores
The idea
Describing a set of scores takes a measure of center and a measure of spread, chosen to fit the data. Put the scores in order. The mean adds the scores and divides by how many there are. The median is the middle score, or the average of the two middle scores. The mode is the most frequent score. The range is the highest score minus the lowest. When one score lies far from the rest, an outlier, the mean moves toward it while the median stays put, so the median describes the typical student better.
In practice
Worked example: seven quiz scores are 12, 14, 15, 15, 16, 18 and 22. They add to 112, so the mean is 16; the median, the fourth score, is 15; the mode is 15; the range is 22 minus 12, or 10. Now replace the 22 with a 50. The total becomes 140 and the mean rises to 20, but the median is still 15, and the range jumps to 38.
Where people slip
Report the median when scores include outliers, and always pair a center with a spread: a mean alone hides whether scores cluster tightly or scatter widely. The range depends on only two scores, which is why the standard deviation is the more stable measure of spread.
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