document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173181>Question 1173181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem 2. Below is a list of vertical jumps (in cm) for 24 athletes who compete in various different sports. <BR>\n" );
document.write( "28 45 55 46 70 72 62 32 75 68 74 54 50 62 63 31 55 68 73 55 60 69 68 92\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Part A. Using # of classes = 4, create a frequency table for the given data set, and use your frequency table to construct a histogram. <BR>\n" );
document.write( "Part B. Using the data set above, calculate the quartiles Qi where i = 0, 1, 2, 3, 4, and construct a box-and-whiskers plot for this data set. <BR>\n" );
document.write( "Part C. Calculate the 15th percentile of this data set. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850748 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=850748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's break down each part of this data analysis problem.\r<BR>\n" );
document.write( "\n" );
document.write( "**Part A: Frequency Table and Histogram**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Determine the Range:**<BR>\n" );
document.write( "    * Maximum value: 92<BR>\n" );
document.write( "    * Minimum value: 28<BR>\n" );
document.write( "    * Range: 92 - 28 = 64\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Determine Class Width:**<BR>\n" );
document.write( "    * Number of classes: 4<BR>\n" );
document.write( "    * Approximate class width: 64 / 4 = 16<BR>\n" );
document.write( "    * To make it easier, let's round up to a class width of 17.\r<BR>\n" );
document.write( "\n" );
document.write( "3.  **Determine Class Limits:**<BR>\n" );
document.write( "    * Starting with the minimum value (28), create the class limits:<BR>\n" );
document.write( "        * Class 1: 28 - (28 + 16) 44<BR>\n" );
document.write( "        * Class 2: 45 - (45 + 16) 61<BR>\n" );
document.write( "        * Class 3: 62 - (62 + 16) 78<BR>\n" );
document.write( "        * Class 4: 79 - (79 + 16) 95\r<BR>\n" );
document.write( "\n" );
document.write( "4.  **Create the Frequency Table:**\r<BR>\n" );
document.write( "\n" );
document.write( "    | Class     | Class Limits | Tally      | Frequency |<BR>\n" );
document.write( "    | --------- | ------------ | ---------- | --------- |<BR>\n" );
document.write( "    | Class 1   | 28 - 44      | II         | 2         |<BR>\n" );
document.write( "    | Class 2   | 45 - 61      | IIIIIIII   | 8         |<BR>\n" );
document.write( "    | Class 3   | 62 - 78      | IIIIIIIIII | 10        |<BR>\n" );
document.write( "    | Class 4   | 79 - 95      | IIII       | 4         |\r<BR>\n" );
document.write( "\n" );
document.write( "5.  **Construct the Histogram:**\r<BR>\n" );
document.write( "\n" );
document.write( "    * X-axis: Class Limits<BR>\n" );
document.write( "    * Y-axis: Frequency<BR>\n" );
document.write( "    * Draw bars with heights corresponding to the frequencies of each class.\r<BR>\n" );
document.write( "\n" );
document.write( "Here's a text-based representation of what the histogram would look like:\r<BR>\n" );
document.write( "\n" );
document.write( "```<BR>\n" );
document.write( "Frequency<BR>\n" );
document.write( "10 | **********<BR>\n" );
document.write( " 9 |<BR>\n" );
document.write( " 8 | ********<BR>\n" );
document.write( " 7 |<BR>\n" );
document.write( " 6 |<BR>\n" );
document.write( " 5 |<BR>\n" );
document.write( " 4 | ****<BR>\n" );
document.write( " 3 |<BR>\n" );
document.write( " 2 | **<BR>\n" );
document.write( " 1 |<BR>\n" );
document.write( "   ---------------------------------<BR>\n" );
document.write( "     28-44 45-61 62-78 79-95 Class Limits<BR>\n" );
document.write( "```\r<BR>\n" );
document.write( "\n" );
document.write( "**Part B: Quartiles and Box-and-Whiskers Plot**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Order the Data:**<BR>\n" );
document.write( "    * 28, 31, 32, 45, 46, 50, 54, 55, 55, 55, 60, 62, 62, 63, 68, 68, 68, 69, 70, 72, 73, 74, 75, 92\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Calculate Quartiles:**<BR>\n" );
document.write( "    * n = 24 (number of data points)<BR>\n" );
document.write( "    * Q1 (25th percentile): (n + 1) * 0.25 = 25 * 0.25 = 6.25, so Q1 is between the 6th and 7th values: (50 + 54) / 2 = 52<BR>\n" );
document.write( "    * Q2 (50th percentile, median): (n + 1) * 0.5 = 25 * 0.5 = 12.5, so Q2 is between the 12th and 13th values: (62 + 62) / 2 = 62<BR>\n" );
document.write( "    * Q3 (75th percentile): (n + 1) * 0.75 = 25 * 0.75 = 18.75, so Q3 is between the 18th and 19th values: (69 + 70) / 2 = 69.5<BR>\n" );
document.write( "    * Q0 (minimum): 28<BR>\n" );
document.write( "    * Q4 (maximum): 92\r<BR>\n" );
document.write( "\n" );
document.write( "3.  **Construct the Box-and-Whiskers Plot:**\r<BR>\n" );
document.write( "\n" );
document.write( "    * Draw a number line that covers the range of your data.<BR>\n" );
document.write( "    * Draw a box from Q1 (52) to Q3 (69.5).<BR>\n" );
document.write( "    * Draw a line inside the box at Q2 (62).<BR>\n" );
document.write( "    * Draw a line (whisker) from Q1 to the minimum value (28).<BR>\n" );
document.write( "    * Draw a line (whisker) from Q3 to the maximum value (92).\r<BR>\n" );
document.write( "\n" );
document.write( "**Part C: 15th Percentile**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Calculate the Position:**<BR>\n" );
document.write( "    * (n + 1) * 0.15 = 25 * 0.15 = 3.75\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Find the Value:**<BR>\n" );
document.write( "    * The 15th percentile is between the 3rd and 4th values.<BR>\n" );
document.write( "    * 3rd value: 32<BR>\n" );
document.write( "    * 4th value: 45<BR>\n" );
document.write( "    * Interpolate: 32 + 0.75 * (45 - 32) = 32 + 0.75 * 13 = 32 + 9.75 = 41.75\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the 15th percentile is approximately 41.75 cm.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );