document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181511>Question 1181511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dennis and Christine scored 32 and 23, respectively, in the National Career Assessment Examination (NCAE). The determining factor for a college scholarship is that a student's score should be in top 10% of the scores of his/her graduating class. The students in the graduating class obtained the following scores in the NCAE<BR>\n" );
document.write( "Suppose that the given data is written in table<BR>\n" );
document.write( "NCAE Scores     f(frequency)       LB        <cf<BR>\n" );
document.write( "39-41               6<BR>\n" );
document.write( "36-38               7<BR>\n" );
document.write( "33-35               9<BR>\n" );
document.write( "30-32               13<BR>\n" );
document.write( "27-29               22 <BR>\n" );
document.write( "24-26               10<BR>\n" );
document.write( "21-23                9<BR>\n" );
document.write( "18-20                7<BR>\n" );
document.write( "15-17                8         <BR>\n" );
document.write( "12-14                4<BR>\n" );
document.write( "9-11                 2<BR>\n" );
document.write( "6-8                  1<BR>\n" );
document.write( "3-5                  1\r<BR>\n" );
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document.write( "Question<BR>\n" );
document.write( "1. Complete the table by filling the LB or the lower boundaries and <cf or the less that cumulative frequency. Explain how you arrive at your answer<BR>\n" );
document.write( "2. Find the 3rd quartile, 72nd percentile and the 8th decile of the set of data<BR>\n" );
document.write( "3. What is the percentile rank of Dennis and Christine\r<BR>\n" );
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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 #850006 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=850006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's the solution:\r<BR>\n" );
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document.write( "**1. Completed Table:**\r<BR>\n" );
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document.write( "To find the lower boundaries (LB), subtract 0.5 from each lower class limit.\r<BR>\n" );
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document.write( "| NCAE Scores | f (frequency) | LB    |<BR>\n" );
document.write( "|-------------|---------------|-------|<BR>\n" );
document.write( "| 39-41       | 6             | 38.5  |<BR>\n" );
document.write( "| 36-38       | 7             | 35.5  |<BR>\n" );
document.write( "| 33-35       | 9             | 32.5  |<BR>\n" );
document.write( "| 30-32       | 13            | 29.5  |<BR>\n" );
document.write( "| 27-29       | 22            | 26.5  |<BR>\n" );
document.write( "| 24-26       | 10            | 23.5  |<BR>\n" );
document.write( "| 21-23       | 9             | 20.5  |<BR>\n" );
document.write( "| 18-20       | 7             | 17.5  |<BR>\n" );
document.write( "| 15-17       | 8             | 14.5  |<BR>\n" );
document.write( "| 12-14       | 4             | 11.5  |<BR>\n" );
document.write( "| 9-11        | 2             | 8.5   |<BR>\n" );
document.write( "| 6-8         | 1             | 5.5   |<BR>\n" );
document.write( "| 3-5         | 1             | 2.5   |\r<BR>\n" );
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document.write( "**2. 3rd Quartile (Q3), 72nd Percentile (P72), and 8th Decile (D8):**\r<BR>\n" );
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document.write( "First, find the cumulative frequency (cf):\r<BR>\n" );
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document.write( "| NCAE Scores | f  | cf |<BR>\n" );
document.write( "|-------------|----|----|<BR>\n" );
document.write( "| 39-41       | 6  | 88 |<BR>\n" );
document.write( "| 36-38       | 7  | 82 |<BR>\n" );
document.write( "| 33-35       | 9  | 75 |<BR>\n" );
document.write( "| 30-32       | 13 | 66 |<BR>\n" );
document.write( "| 27-29       | 22 | 53 |<BR>\n" );
document.write( "| 24-26       | 10 | 31 |<BR>\n" );
document.write( "| 21-23       | 9  | 21 |<BR>\n" );
document.write( "| 18-20       | 7  | 12 |<BR>\n" );
document.write( "| 15-17       | 8  | 5  |<BR>\n" );
document.write( "| 12-14       | 4  | 1  |<BR>\n" );
document.write( "| 9-11        | 2  | 1  |<BR>\n" );
document.write( "| 6-8         | 1  | 1  |<BR>\n" );
document.write( "| 3-5         | 1  | 1  |\r<BR>\n" );
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document.write( "*   **Q3:** Q3 is the 75th percentile.  (75/100) * 88 = 66. The 66th value falls in the 33-35 class.\r<BR>\n" );
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document.write( "    Q3 = LB + [( (75/100) * N - cf_below ) / f_class ] * class_width<BR>\n" );
document.write( "    Q3 = 32.5 + [ (66 - 53) / 9 ] * 3<BR>\n" );
document.write( "    Q3 = 32.5 + 4.33 = 36.83\r<BR>\n" );
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document.write( "*   **P72:** (72/100) * 88 = 63.36. The 63.36th value falls in the 30-32 class.\r<BR>\n" );
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document.write( "    P72 = 29.5 + [(63.36 - 53) / 13] * 3<BR>\n" );
document.write( "    P72 = 29.5 + 2.41 = 31.91\r<BR>\n" );
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document.write( "*   **D8:** (8/10) * 88 = 70.4. The 70.4th value falls in the 33-35 class.\r<BR>\n" );
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document.write( "    D8 = 32.5 + [(70.4 - 53) / 9] * 3<BR>\n" );
document.write( "    D8 = 32.5 + 5.8 = 38.3\r<BR>\n" );
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document.write( "**3. Percentile Rank of Dennis and Christine:**\r<BR>\n" );
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document.write( "*   **Dennis (score 32):** Dennis's score falls in the 30-32 class.\r<BR>\n" );
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document.write( "    Percentile Rank = [ (cf_below + 0.5 * f_class) / N ] * 100<BR>\n" );
document.write( "    Percentile Rank = [ (53 + 0.5 * 13) / 88 ] * 100<BR>\n" );
document.write( "    Percentile Rank = [ (53 + 6.5) / 88 ] * 100<BR>\n" );
document.write( "    Percentile Rank = (59.5 / 88) * 100 ≈ 67.61\r<BR>\n" );
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document.write( "*   **Christine (score 23):** Christine's score falls in the 21-23 class.\r<BR>\n" );
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document.write( "    Percentile Rank = [ (21 + 0.5 * 9) / 88 ] * 100<BR>\n" );
document.write( "    Percentile Rank = [ (21 + 4.5) / 88 ] * 100<BR>\n" );
document.write( "    Percentile Rank = (25.5 / 88) * 100 ≈ 28.98<BR>\n" );
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