To find the mean of a class's test scores, we need to add all
the test scores from that class and divide by the number of tests. The mean
takes every score into account and so is affected by extremely high scores and
extremely low scores.
Let's find the means (or the averages) for two
classes:
Class 1:
85 + 90 + 78 + 54 + 88 + 76 + 83 + 99 + 49 + 93 + 76 + 90 + 78 + 55 + 89 +
76 + 65 + 81 + 89 + 91 =
20
(Mean for Class 1) 
Class 2:
76+ 80+ 59+ 89+ 92+ 68+ 55+ 77+ 98+ 95+ 80+ 90+ 96+ 80+ 78+
65+ 77+ 92+ 89+ 60
20
(Mean for Class 2) 
What does this mean? An "average"
student in Class 1 scored a 79.25 and an "average" student in Class 2 scored a
79.8. Based on the means, the two classes performed similarly on the
test.
Notice that the averages, 79.25 and 79.8, are not equal to any
of the test scores. Averages do not have to equal one of the values that
it represents. An average just gives us a "general" picture of the values it
represents.
