document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172923>Question 1172923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Compute the median and mode of the following distribution<BR>\n" );
document.write( "Marks 10-19 20-29 30-39 40-49 50-59<BR>\n" );
document.write( "No. of students 5 25 40 20 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850797 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Median**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Find the cumulative frequency:**<BR>\n" );
document.write( "    * 10-19: 5<BR>\n" );
document.write( "    * 20-29: 5 + 25 = 30<BR>\n" );
document.write( "    * 30-39: 30 + 40 = 70<BR>\n" );
document.write( "    * 40-49: 70 + 20 = 90<BR>\n" );
document.write( "    * 50-59: 90 + 10 = 100\r<BR>\n" );
document.write( "\n" );
document.write( "* **Identify the median class:**<BR>\n" );
document.write( "    * The total number of students is 100.<BR>\n" );
document.write( "    * The median is the value that divides the data into two equal halves, so we need the 50th value.<BR>\n" );
document.write( "    * The cumulative frequency that includes the 50th value is 70, which corresponds to the 30-39 class.\r<BR>\n" );
document.write( "\n" );
document.write( "* **Calculate the median:**<BR>\n" );
document.write( "    * Median = L + [(N/2 - CF) / f] * h<BR>\n" );
document.write( "        * L = lower limit of the median class = 30<BR>\n" );
document.write( "        * N = total number of students = 100<BR>\n" );
document.write( "        * CF = cumulative frequency of the class before the median class = 30<BR>\n" );
document.write( "        * f = frequency of the median class = 40<BR>\n" );
document.write( "        * h = class width = 10<BR>\n" );
document.write( "    * Median = 30 + [(100/2 - 30) / 40] * 10<BR>\n" );
document.write( "    * Median = 30 + (20/40) * 10<BR>\n" );
document.write( "    * Median = 30 + 5<BR>\n" );
document.write( "    * **Median = 35**\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Mode**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Identify the modal class:**<BR>\n" );
document.write( "    * The modal class is the class with the highest frequency.<BR>\n" );
document.write( "    * In this case, the modal class is 30-39 with a frequency of 40.\r<BR>\n" );
document.write( "\n" );
document.write( "* **Calculate the mode:**<BR>\n" );
document.write( "    * Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] * h<BR>\n" );
document.write( "        * L = lower limit of the modal class = 30<BR>\n" );
document.write( "        * f1 = frequency of the modal class = 40<BR>\n" );
document.write( "        * f0 = frequency of the class before the modal class = 25<BR>\n" );
document.write( "        * f2 = frequency of the class after the modal class = 20<BR>\n" );
document.write( "        * h = class width = 10<BR>\n" );
document.write( "    * Mode = 30 + [(40 - 25) / (2 * 40 - 25 - 20)] * 10<BR>\n" );
document.write( "    * Mode = 30 + (15 / 35) * 10<BR>\n" );
document.write( "    * Mode = 30 + 4.29<BR>\n" );
document.write( "    * **Mode = 34.29**\r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Median = 35**<BR>\n" );
document.write( "* **Mode = 34.29** </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );