1993 AMC 8 Problem 11

Below is the professionally curated solution for Problem 11 of the 1993 AMC 8, 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.

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Concepts:median (data)data and graph interpretation

Difficulty rating: 800

11.

Consider this histogram of the scores for $81$ students taking a test. The median is in the interval labeled which value?

$60$

$65$

$70$

$75$

$80$

Solution:

Since $81$ students took the test, the median is the $41$ st score counting up from the lowest.

Adding the bar heights from the left gives running totals $1, 3, 7, 12, 18, 28, 42, \ldots$ The total first passes $41$ at the interval labeled $70,$ which contains the $29$ th through $42$ nd scores. So the $41$ st score lies in the interval labeled $70.$

Thus, the correct answer is C .

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