1993 AMC 8 Problem 11

Attempt Problem 11 of the 1993 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

Consider this histogram of the scores for 8181 students taking a test. The median is in the interval labeled which value?
6060
6565
7070
7575
8080
Answer: C
Concepts:median (data)data and graph interpretation
Small hint:
With 8181 scores in order, the median is the middle one: the 4141st score counting from the lowest
Big hint:
Add the bar heights from left to right until the running total first reaches 4141
Solution:
Since 8181 students took the test, the median is the 4141st score counting up from the lowest.
Adding the bar heights from the left gives running totals 1,1, 3,3, 7,7, 12,12, 18,18, 28,28, 42,42, …\ldots The total first passes 4141 at the interval labeled 70,70, which contains the 2929th through 4242nd scores. So the 4141st score lies in the interval labeled 70.70.
Thus, the correct answer is C .
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