document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028398>Question 1028398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two groups of students took a certain test with possible scores 1,2,3,4,5,6,7,8,9,10.\r<BR>\n" );
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document.write( "(a) The &#64257;rst group consisted of 300 students; 9% of the students scored 5, 42% scored 6, 5% scored 7 and the remaining 44% scored 8. Calculate the average score of this group. Also, calculate the median and the mode.\r<BR>\n" );
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document.write( "(b) A second group of 150 students also took the test. The only scores this group of students obtained were 5 and 7. The average score was 6.44. How many students scored 5 for the test? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643495 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=643495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) The &#64257;rst group consisted of 300 students: <BR>\n" );
document.write( "9% of the students scored 5 (27 students) <BR>\n" );
document.write( "42% scored 6 (126 students)<BR>\n" );
document.write( "5% scored 7 (15 students)<BR>\n" );
document.write( "44% scored 8 (132 students).\r<BR>\n" );
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document.write( "The mode is clearly 8, because it was the most frequently appearing score.<BR>\n" );
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document.write( "The median is 6.  To see this, arrange the scores in increasing order.  The median would be the average of the 150th and 151st values, which is clearly 6.\r<BR>\n" );
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document.write( "The average score (mean) of the group is 5*0.09 + 6*0.42 + 7*0.05 + 8*0.44 = 6.84.\r<BR>\n" );
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document.write( "(b) Let x = # of students who scored 5 ==> 150-x = # of students who scored 7.<BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B7%28150-x%29%29%2F150+=+6.44 ALIGN=MIDDLE  ALT=\"%285x%2B7%28150-x%29%29%2F150+=+6.44\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<==> 5x + 1,050 -7x = 966\r<BR>\n" );
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document.write( "==> -2x = -84\r<BR>\n" );
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document.write( "==> x = 42, the number of students that scored 5. </SPAN>\n" );
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