document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205202>Question 1205202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Considering the following distribution for blood pressure level of male patients in a given hospital <BR>\n" );
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document.write( "Values (BP)          Frequency (# of patients)<BR>\n" );
document.write( "140- 150                17<BR>\n" );
document.write( "150- 160                 29<BR>\n" );
document.write( "160- 170                 42<BR>\n" );
document.write( "170- 180                 72<BR>\n" );
document.write( "180- 190                  84<BR>\n" );
document.write( "190- 200                 107<BR>\n" );
document.write( "200- 210                 49<BR>\n" );
document.write( "210- 220                 34<BR>\n" );
document.write( "220- 230                 31<BR>\n" );
document.write( "230- 240                 16<BR>\n" );
document.write( "240- 250                 12<BR>\n" );
document.write( "Calculate:<BR>\n" );
document.write( "a) All the quartiles.<BR>\n" );
document.write( "b) Find the 8th deciles.<BR>\n" );
document.write( "c) Find the 20th percentiles </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847963 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</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=847963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To calculate the quartiles, deciles, and percentiles, we first need to create a cumulative frequency distribution table:\r<BR>\n" );
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document.write( "| Blood Pressure (BP) | Frequency (f) | Cumulative Frequency (cf) |<BR>\n" );
document.write( "|---|---|---|<BR>\n" );
document.write( "| 140-150 | 17 | 17 |<BR>\n" );
document.write( "| 150-160 | 29 | 46 |<BR>\n" );
document.write( "| 160-170 | 42 | 88 |<BR>\n" );
document.write( "| 170-180 | 72 | 160 |<BR>\n" );
document.write( "| 180-190 | 84 | 244 |<BR>\n" );
document.write( "| 190-200 | 107 | 351 |<BR>\n" );
document.write( "| 200-210 | 49 | 400 |<BR>\n" );
document.write( "| 210-220 | 34 | 434 |<BR>\n" );
document.write( "| 220-230 | 31 | 465 |<BR>\n" );
document.write( "| 230-240 | 16 | 481 |<BR>\n" );
document.write( "| 240-250 | 12 | 493 |\r<BR>\n" );
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document.write( "**Total Frequency (N) = 493**\r<BR>\n" );
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document.write( "### a) Quartiles\r<BR>\n" );
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document.write( "* **Q1 (First Quartile):** <BR>\n" );
document.write( "  * Position of Q1 = N/4 = 493/4 ≈ 123.25<BR>\n" );
document.write( "  * Q1 lies in the 4th class interval (170-180).<BR>\n" );
document.write( "  * Using interpolation, Q1 = 170 + [(123.25 - 88) / 72] * 10 ≈ 175.18\r<BR>\n" );
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document.write( "* **Q2 (Second Quartile or Median):** <BR>\n" );
document.write( "  * Position of Q2 = N/2 = 493/2 ≈ 246.5<BR>\n" );
document.write( "  * Q2 lies in the 6th class interval (190-200).<BR>\n" );
document.write( "  * Using interpolation, Q2 = 190 + [(246.5 - 244) / 107] * 10 ≈ 190.23\r<BR>\n" );
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document.write( "* **Q3 (Third Quartile):**<BR>\n" );
document.write( "  * Position of Q3 = 3N/4 = 3*493/4 ≈ 369.75<BR>\n" );
document.write( "  * Q3 lies in the 7th class interval (200-210).<BR>\n" );
document.write( "  * Using interpolation, Q3 = 200 + [(369.75 - 351) / 49] * 10 ≈ 203.78\r<BR>\n" );
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document.write( "### b) 8th Decile\r<BR>\n" );
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document.write( "* Position of the 8th decile = 8N/10 = 8*493/10 ≈ 394.4<BR>\n" );
document.write( "* The 8th decile lies in the 7th class interval (200-210).<BR>\n" );
document.write( "* Using interpolation, 8th decile = 200 + [(394.4 - 351) / 49] * 10 ≈ 208.86\r<BR>\n" );
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document.write( "### c) 20th Percentile \r<BR>\n" );
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document.write( "* Position of the 20th percentile = 20N/100 = 20*493/100 ≈ 98.6<BR>\n" );
document.write( "* The 20th percentile lies in the 3rd class interval (160-170).<BR>\n" );
document.write( "* Using interpolation, 20th percentile = 160 + [(98.6 - 88) / 42] * 10 ≈ 162.52<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );