document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192782>Question 1192782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . The table  below shows the frequency distribution of the masses of 52 female students at a college. Measurements have been recorded to the nearest Kilogram Mass (Kg) Frequency 40-44 3 45-49 2 50-54 7 55-59 18 60-64 18 65-69 3 70-74 1<BR>\n" );
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document.write( "i. Construct a cumulative frequency table and draw a cumulative frequency curve ii. How many students weighed less than 57Kg? <BR>\n" );
document.write( "iii. How many students weighed more than 61Kg? <BR>\n" );
document.write( "iv. 20% were heavier than x Kg. Find the value of  <BR>\n" );
document.write( " v. Estimate the median<BR>\n" );
document.write( " vi. Estimate the interquartile range   4. The frequency distribution shows the number of  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848950 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=848950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **i. Construct a Cumulative Frequency Table:**\r<BR>\n" );
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document.write( "| Mass (Kg) | Frequency | Cumulative Frequency |<BR>\n" );
document.write( "|---|---|---|<BR>\n" );
document.write( "| 40-44 | 3 | 3 |<BR>\n" );
document.write( "| 45-49 | 2 | 5 |<BR>\n" );
document.write( "| 50-54 | 7 | 12 |<BR>\n" );
document.write( "| 55-59 | 18 | 30 |<BR>\n" );
document.write( "| 60-64 | 18 | 48 |<BR>\n" );
document.write( "| 65-69 | 3 | 51 |<BR>\n" );
document.write( "| 70-74 | 1 | 52 |\r<BR>\n" );
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document.write( "**ii. How many students weighed less than 57Kg?**\r<BR>\n" );
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document.write( "* From the cumulative frequency table, we see that 30 students weighed less than 57Kg.\r<BR>\n" );
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document.write( "**iii. How many students weighed more than 61Kg?**\r<BR>\n" );
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document.write( "* Total students = 52<BR>\n" );
document.write( "* Students weighing less than or equal to 61Kg = 48 (from the cumulative frequency table)<BR>\n" );
document.write( "* Students weighing more than 61Kg = Total students - Students weighing less than or equal to 61Kg = 52 - 48 = 4 students\r<BR>\n" );
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document.write( "**iv. 20% were heavier than x Kg. Find the value of x**\r<BR>\n" );
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document.write( "* 20% of the students = 0.20 * 52 = 10.4 students <BR>\n" );
document.write( "* Since we are dealing with whole numbers, we can round up to 11 students. <BR>\n" );
document.write( "* From the cumulative frequency table, we can see that 41 students weigh less than or equal to 64Kg. <BR>\n" );
document.write( "* Therefore, 52 - 41 = 11 students weigh more than 64Kg.<BR>\n" );
document.write( "* Hence, x = 64Kg\r<BR>\n" );
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document.write( "**v. Estimate the median**\r<BR>\n" );
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document.write( "* Median is the middle value when the data is arranged in ascending order. <BR>\n" );
document.write( "* Since there are 52 students, the median lies between the 26th and 27th student. <BR>\n" );
document.write( "* From the cumulative frequency table, we see that the 26th and 27th students fall within the 55-59Kg class. <BR>\n" );
document.write( "* **Therefore, the estimated median lies within the 55-59Kg class.**\r<BR>\n" );
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document.write( "**vi. Estimate the interquartile range**\r<BR>\n" );
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document.write( "* **Find the first quartile (Q1):**<BR>\n" );
document.write( "    * 25% of 52 students = 13 students<BR>\n" );
document.write( "    * Q1 lies within the 50-54Kg class.\r<BR>\n" );
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document.write( "* **Find the third quartile (Q3):**<BR>\n" );
document.write( "    * 75% of 52 students = 39 students<BR>\n" );
document.write( "    * Q3 lies within the 60-64Kg class.\r<BR>\n" );
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document.write( "* **Estimate the interquartile range (IQR):**<BR>\n" );
document.write( "    * IQR = Q3 - Q1 <BR>\n" );
document.write( "    * IQR ≈ (Upper limit of 60-64Kg class - Lower limit of 50-54Kg class) <BR>\n" );
document.write( "    * IQR ≈ 64.5 - 49.5 = 15Kg\r<BR>\n" );
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document.write( "**Note:** These are estimates based on the grouped data. For more precise calculations, you would need the individual weight measurements of each student.\r<BR>\n" );
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document.write( "I hope this helps! Let me know if you have any other questions.<BR>\n" );
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