document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=874244>Question 874244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the median and range of the given data set?\r<BR>\n" );
document.write( "\n" );
document.write( "10,25,40,35,15,5,20,30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527396 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=527396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sort out the data set:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5, 10, 15, 20, 25, 30, 35, 40\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 8 values. This is an even number of values. So the median will be in between the two middle-most numbers (the median may or may not be in the list -- there are no guarantees).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "More specifically, the median will be in between the elements at slot numbers 4 and 5 (divide 8 in half to get 4).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means you can count 4 places over to get to the value of 20. The next number over is 25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The median will be the average of the two values 20 and 25. So average them to get (20 + 25)/2 = (45)/2 = 22.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or you can do it this way\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1) Start with the list of numbers shown below\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5, 10, 15, 20, 25, 30, 35, 40\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Step 2) Erase the outer pair of numbers (5 on the very left and 40 on the very right) to get the new list:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10, 15, 20, 25, 30, 35\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Repeat this until the list reduces to exactly two values.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Step 3) Erase the outer pair of numbers (10 on the very left and 35 on the very right) to get the new list:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "15, 20, 25, 30\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Step 4) Erase the outer pair of numbers (15 on the very left and 30 on the very right) to get the new list:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "20, 25\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're left with exactly two numbers: 20 and 25. So we are done erasing values.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Average the two values to get (20 + 25)/2 = (45)/2 = 22.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the median is 22.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------------------------<BR>\n" );
document.write( "----------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The range is equal to the difference in the largest value and smallest value\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Range = Max - Min\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Range = 40 - 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Range = 35 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );