https://artofproblemsolving.com/wiki/index.php?title=1993_AJHSME_Problems/Problem_11&feed=atom&action=history
1993 AJHSME Problems/Problem 11 - Revision history
2024-03-29T14:26:20Z
Revision history for this page on the wiki
MediaWiki 1.31.1
https://artofproblemsolving.com/wiki/index.php?title=1993_AJHSME_Problems/Problem_11&diff=55656&oldid=prev
Nathan wailes at 04:11, 5 July 2013
2013-07-05T04:11:21Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 04:11, 5 July 2013</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{AJHSME box|year=1993|num-b=10|num-a=12}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{AJHSME box|year=1993|num-b=10|num-a=12}}</div></td></tr>
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Nathan wailes
https://artofproblemsolving.com/wiki/index.php?title=1993_AJHSME_Problems/Problem_11&diff=50031&oldid=prev
Gina at 02:36, 23 December 2012
2012-12-23T02:36:33Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 02:36, 23 December 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== Problem <del class="diffchange diffchange-inline">11 </del>==</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== Problem ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Consider this histogram of the scores for <math>81</math> students taking a test:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Consider this histogram of the scores for <math>81</math> students taking a test:</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l79" >Line 79:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Since <math> 81 </math> students took the test, the median is the score of the <math> 41^{st} </math> student, which is <math> \boxed{\text{(C)}\ 70} </math>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Since <math> 81 </math> students took the test, the median is the score of the <math> 41^{st} </math> student<ins class="diffchange diffchange-inline">. The five rightmost intervals include <math>2+3+6+12+16=39</math> students, so the <math>41^{st}</math> one must lie in the next interval</ins>, which is <math> \boxed{\text{(C)}\ 70} </math>.</div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==See Also==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{AJHSME box|year=1993|num-b=10|num-a=12}}</ins></div></td></tr>
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Gina
https://artofproblemsolving.com/wiki/index.php?title=1993_AJHSME_Problems/Problem_11&diff=40877&oldid=prev
Math Kirby: Created page with "== Problem 11 == Consider this histogram of the scores for <math>81</math> students taking a test: <asy> unitsize(12); draw((0,0)--(26,0)); draw((1,1)--(25,1)); draw((3,2)--(25..."
2011-07-29T16:12:24Z
<p>Created page with "== Problem 11 == Consider this histogram of the scores for <math>81</math> students taking a test: <asy> unitsize(12); draw((0,0)--(26,0)); draw((1,1)--(25,1)); draw((3,2)--(25..."</p>
<p><b>New page</b></p><div>== Problem 11 ==<br />
<br />
Consider this histogram of the scores for <math>81</math> students taking a test:<br />
<br />
<asy><br />
unitsize(12);<br />
draw((0,0)--(26,0));<br />
draw((1,1)--(25,1));<br />
draw((3,2)--(25,2));<br />
draw((5,3)--(23,3));<br />
draw((5,4)--(21,4));<br />
draw((7,5)--(21,5));<br />
draw((9,6)--(21,6));<br />
draw((11,7)--(19,7));<br />
draw((11,8)--(19,8));<br />
draw((11,9)--(19,9));<br />
draw((11,10)--(19,10));<br />
draw((13,11)--(19,11));<br />
draw((13,12)--(19,12));<br />
draw((13,13)--(17,13));<br />
draw((13,14)--(17,14));<br />
draw((15,15)--(17,15));<br />
draw((15,16)--(17,16));<br />
<br />
draw((1,0)--(1,1));<br />
draw((3,0)--(3,2));<br />
draw((5,0)--(5,4));<br />
draw((7,0)--(7,5));<br />
draw((9,0)--(9,6));<br />
draw((11,0)--(11,10));<br />
draw((13,0)--(13,14));<br />
draw((15,0)--(15,16));<br />
draw((17,0)--(17,16));<br />
draw((19,0)--(19,12));<br />
draw((21,0)--(21,6));<br />
draw((23,0)--(23,3));<br />
draw((25,0)--(25,2));<br />
<br />
for (int a = 1; a < 13; ++a)<br />
{<br />
draw((2*a,-.25)--(2*a,.25));<br />
}<br />
<br />
label("$40$",(2,-.25),S);<br />
label("$45$",(4,-.25),S);<br />
label("$50$",(6,-.25),S);<br />
label("$55$",(8,-.25),S);<br />
label("$60$",(10,-.25),S);<br />
label("$65$",(12,-.25),S);<br />
label("$70$",(14,-.25),S);<br />
label("$75$",(16,-.25),S);<br />
label("$80$",(18,-.25),S);<br />
label("$85$",(20,-.25),S);<br />
label("$90$",(22,-.25),S);<br />
label("$95$",(24,-.25),S);<br />
<br />
label("$1$",(2,1),N);<br />
label("$2$",(4,2),N);<br />
label("$4$",(6,4),N);<br />
label("$5$",(8,5),N);<br />
label("$6$",(10,6),N);<br />
label("$10$",(12,10),N);<br />
label("$14$",(14,14),N);<br />
label("$16$",(16,16),N);<br />
label("$12$",(18,12),N);<br />
label("$6$",(20,6),N);<br />
label("$3$",(22,3),N);<br />
label("$2$",(24,2),N);<br />
<br />
label("Number",(4,8),N);<br />
label("of Students",(4,7),N);<br />
<br />
label("$\textbf{STUDENT TEST SCORES}$",(14,18),N);<br />
</asy><br />
<br />
The median is in the interval labeled <br />
<br />
<math>\text{(A)}\ 60 \qquad \text{(B)}\ 65 \qquad \text{(C)}\ 70 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 80</math><br />
<br />
==Solution==<br />
Since <math> 81 </math> students took the test, the median is the score of the <math> 41^{st} </math> student, which is <math> \boxed{\text{(C)}\ 70} </math>.</div>
Math Kirby