document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157998>Question 1157998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results are:\r<BR>\n" );
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document.write( "Aptitude Score	0	1	2	3	4	5\r<BR>\n" );
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document.write( "Frequency       0	4	1	5	1	3\r<BR>\n" );
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document.write( "Round the mean to the nearest hundredth.\r<BR>\n" );
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document.write( "The mean (average) aptitude score is \r<BR>\n" );
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document.write( "The median aptitude score is \r<BR>\n" );
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document.write( "Thank you in advance.<BR>\n" );
document.write( "SYL\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854538 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C7%2C%0D%0AScore%2Cred%280%29%2Cred%281%29%2Cred%282%29%2Cred%283%29%2Cred%284%29%2Cred%285%29%2C%0D%0AFrequency%2Cgreen%280%29%2Cgreen%284%29%2Cgreen%281%29%2Cgreen%285%29%2Cgreen%281%29%2Cgreen%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I see that<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%280%29 ALIGN=MIDDLE  ALT=\"green%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > students got a score of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%280%29 ALIGN=MIDDLE  ALT=\"red%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%284%29 ALIGN=MIDDLE  ALT=\"green%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > students got a score of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29 ALIGN=MIDDLE  ALT=\"red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%281%29 ALIGN=MIDDLE  ALT=\"green%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > student got a score of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%282%29 ALIGN=MIDDLE  ALT=\"red%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%285%29 ALIGN=MIDDLE  ALT=\"green%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > students got a score of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29 ALIGN=MIDDLE  ALT=\"red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%281%29 ALIGN=MIDDLE  ALT=\"green%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > student got a score of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%284%29 ALIGN=MIDDLE  ALT=\"red%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%283%29 ALIGN=MIDDLE  ALT=\"green%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > students got a score of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%285%29 ALIGN=MIDDLE  ALT=\"red%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That means the number of students was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%284%29%2Bgreen%281%29%2Bgreen%285%29%2Bgreen%281%29%2Bgreen%283%29=14 ALIGN=MIDDLE  ALT=\"green%284%29%2Bgreen%281%29%2Bgreen%285%29%2Bgreen%281%29%2Bgreen%283%29=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The mean is the average of all those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+scores ALIGN=MIDDLE  ALT=\"14+scores\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "To calculate it I have to add those 14 scores.<BR>\n" );
document.write( "I could add<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29%2Bred%281%29%2Bred%281%29%2Bred%281%29%2Bred%282%29%2Bred%283%29%2Bred%283%29%2Bred%283%29%2Bred%283%29%2Bred%283%29%2B%22...%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "However, instead of add a score several times, I could just multiply times its frequency, and add the products:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28red%281%29%2Agreen%284%29%29%2B%28red%282%29%2Agreen%281%29%29%2B%28red%283%29%2Agreen%285%29%29%2B%28red%284%29%2Agreen%281%29%29%2B%28red%285%29%2Agreen%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Oh! And because centuries ago people doing math all over the world decided to agree that multiplications have priority over addition, I can skip all those parentheses, and write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sum ALIGN=MIDDLE  ALT=\"Sum\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=of ALIGN=MIDDLE  ALT=\"of\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=all ALIGN=MIDDLE  ALT=\"all\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=scores ALIGN=MIDDLE  ALT=\"scores\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29%2Agreen%284%29%2Bred%282%29%2Agreen%281%29%2Bred%283%29%2Agreen%285%29%2Bred%284%29%2Agreen%281%29%2Bred%285%29%2Agreen%283%29=4%2B2%2B15%2B4%2B15=40 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mean=40%2F14=20%2F7=%222.857142857142857142...%22 ALIGN=MIDDLE  ALT=\"mean=40%2F14=20%2F7=%222.857142857142857142...%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Round the mean to the nearest hundredth, it says,<BR>\n" );
document.write( "so it rounds to 2 and 86/100, because the thousands digit is 7, so we have to round up.<BR>\n" );
document.write( "The mean (average) aptitude score is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282.86%29 ALIGN=MIDDLE  ALT=\"highlight%282.86%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "The median of a set of values is the one in the middle when we put the values in order.<BR>\n" );
document.write( "And if there is an even number of value, we average the two in the middle.<BR>\n" );
document.write( "The 14 scores in order are <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29 ALIGN=MIDDLE  ALT=\"red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29 ALIGN=MIDDLE  ALT=\"red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29 ALIGN=MIDDLE  ALT=\"red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29 ALIGN=MIDDLE  ALT=\"red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%282%29 ALIGN=MIDDLE  ALT=\"red%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29%2Cred%283%29%7D%7D%7B%7B%7Bred%283%29 ALIGN=MIDDLE  ALT=\"red%283%29%2Cred%283%29%7D%7D%7B%7B%7Bred%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29 ALIGN=MIDDLE  ALT=\"red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29 ALIGN=MIDDLE  ALT=\"red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%284%29 ALIGN=MIDDLE  ALT=\"red%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%285%29 ALIGN=MIDDLE  ALT=\"red%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%285%29 ALIGN=MIDDLE  ALT=\"red%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%285%29 ALIGN=MIDDLE  ALT=\"red%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "The seventh and eighth values. both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29 ALIGN=MIDDLE  ALT=\"red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , are the two in the middle, and their average is, of course, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29 ALIGN=MIDDLE  ALT=\"red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The median aptitude score is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283%29 ALIGN=MIDDLE  ALT=\"highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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