document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202735>Question 1202735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the following test scores in a class of 34 students: <BR>\n" );
document.write( "56, 60, 60, 61, 62, 63, 65, 66, 70, 70, 72, 73, 74, 74, 75, 75, 78, 78, 79, 80, 81, 85, 86, 87, 88, 88, 89, 89, 90, 94, 99, 99, 100, 100. \r<BR>\n" );
document.write( "\n" );
document.write( "What is the five-number summary? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837808 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "min = 56<BR>\n" );
document.write( "Q1 = 70<BR>\n" );
document.write( "median = 78<BR>\n" );
document.write( "Q3 = 88<BR>\n" );
document.write( "max = 100 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation:<BR>\n" );
document.write( "The first step is to sort the data. <BR>\n" );
document.write( "Luckily that has been done for us already.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are n = 34 values in the set.<BR>\n" );
document.write( "n/2 = 34/2 = 17<BR>\n" );
document.write( "The middle most value is a tie between the values in slots 17 and 18. Those values are 78 and 78. <BR>\n" );
document.write( "There's no need to use the midpoint formula, but you could if you wanted to.<BR>\n" );
document.write( "Median = 78\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We'll split the data into two subsets<BR>\n" );
document.write( "L = lower set = stuff smaller than the median<BR>\n" );
document.write( "U = upper set = stuff larger than the median\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "L = {56, 60, 60, 61, 62, 63, 65, 66, 70, 70, 72, 73, 74, 74, 75, 75, 78}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "U = {78, 79, 80, 81, 85, 86, 87, 88, 88, 89, 89, 90, 94, 99, 99, 100, 100}\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set L has 17 items<BR>\n" );
document.write( "17/2 = 8.5 which rounds to 9<BR>\n" );
document.write( "The value in slot 9 of set L is 70<BR>\n" );
document.write( "Therefore, the median of set L is 70, and it is the first quartile (Q1)<BR>\n" );
document.write( "Q1 = 70\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Through similar steps, the value of Q3 = 88 because it is the median of set U.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The min and max are the smallest and largest elements of the original set. <BR>\n" );
document.write( "min = 56<BR>\n" );
document.write( "max = 100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To wrap things up:<BR>\n" );
document.write( "min = 56<BR>\n" );
document.write( "Q1 = 70<BR>\n" );
document.write( "median = 78<BR>\n" );
document.write( "Q3 = 88<BR>\n" );
document.write( "max = 100<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );