MathDB

11

Part of 1993 AMC 8

Problems(1)

Evaluating the graph of 81 student's test scores

Source: 1993 AMC 8 Problem 11

6/28/2011
Consider this histogram of the scores for 8181 students taking a test:
[asy] unitsize(12); draw((0,0)--(26,0)); draw((1,1)--(25,1)); draw((3,2)--(25,2)); draw((5,3)--(23,3)); draw((5,4)--(21,4)); draw((7,5)--(21,5)); draw((9,6)--(21,6)); draw((11,7)--(19,7)); draw((11,8)--(19,8)); draw((11,9)--(19,9)); draw((11,10)--(19,10)); draw((13,11)--(19,11)); draw((13,12)--(19,12)); draw((13,13)--(17,13)); draw((13,14)--(17,14)); draw((15,15)--(17,15)); draw((15,16)--(17,16));
draw((1,0)--(1,1)); draw((3,0)--(3,2)); draw((5,0)--(5,4)); draw((7,0)--(7,5)); draw((9,0)--(9,6)); draw((11,0)--(11,10)); draw((13,0)--(13,14)); draw((15,0)--(15,16)); draw((17,0)--(17,16)); draw((19,0)--(19,12)); draw((21,0)--(21,6)); draw((23,0)--(23,3)); draw((25,0)--(25,2));
for (int a = 1; a < 13; ++a) { draw((2*a,-.25)--(2*a,.25)); }
label("4040",(2,-.25),S); label("4545",(4,-.25),S); label("5050",(6,-.25),S); label("5555",(8,-.25),S); label("6060",(10,-.25),S); label("6565",(12,-.25),S); label("7070",(14,-.25),S); label("7575",(16,-.25),S); label("8080",(18,-.25),S); label("8585",(20,-.25),S); label("9090",(22,-.25),S); label("9595",(24,-.25),S);
label("11",(2,1),N); label("22",(4,2),N); label("44",(6,4),N); label("55",(8,5),N); label("66",(10,6),N); label("1010",(12,10),N); label("1414",(14,14),N); label("1616",(16,16),N); label("1212",(18,12),N); label("66",(20,6),N); label("33",(22,3),N); label("22",(24,2),N);
label("Number",(4,8),N); label("of Students",(4,7),N);
label("<spanclass=′latex−bold′>STUDENTTESTSCORES</span><span class='latex-bold'>STUDENT TEST SCORES</span>",(14,18),N); [/asy]
The median is in the interval labeled
(A) 60(B) 65(C) 70(D) 75(E) 80\text{(A)}\ 60 \qquad \text{(B)}\ 65 \qquad \text{(C)}\ 70 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 80
AMC