On the day of a test, Margarette was absent. The nineteen students present took the test, and their average score was 70. The next day, Margarette took the test, and after this was graded, the teacher calculated that the average of all twenty students was 72. What was Margarette's grade?
A possible trap answer is 74. We can't assume that Margarette and the rest of the class are equally spaced from the mean, because the sizes are different.
To calculate this, we find the sum:
sum of scores = (average) x (# of students)
Without Margarette, sum = 19x70 = 1330. With Margarette, sum = 20x72 = 1440. Margarette's score is the difference between these: 1440 – 1330 = 110, an impressive score!