document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190560>Question 1190560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marks of 75 students are summarised in the following frequency distribution Marks Frequency 40  -  44 7 45 - 49 10 50  -  54 22 55  -  59 F1 60  -  64 F2 65  -  69 6 70 - 74 3 If 20% of the students have marks b/n 55 and 59 find The 5th deciles, The 60th percentile, 1 quartiles<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822255 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given data table<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Marks</TD><TD >Frequency</TD></tr><tr><TD >40 - 44</TD><TD >7</TD></tr><tr><TD >45 - 49</TD><TD >10</TD></tr><tr><TD >50 - 54</TD><TD >22</TD></tr><tr><TD >55 - 59</TD><TD >F1</TD></tr><tr><TD >60 - 64</TD><TD >F2</TD></tr><tr><TD >65 - 69</TD><TD >6</TD></tr><tr><TD >70 - 74</TD><TD >3</TD></tr>\n" );
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document.write( "We're told that \"20% of the students have marks b/n 55 and 59\" which I'm assuming the b/n means \"between\".\r<BR>\n" );
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document.write( "If 20% of the marks are between 55 and 59, then <BR>\n" );
document.write( "20% of 75 = 0.20*75 = 15 <BR>\n" );
document.write( "This means 15 students are in the interval 55 - 59<BR>\n" );
document.write( "We'll replace the F1 with 15<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Marks</TD><TD >Frequency</TD></tr><tr><TD >40 - 44</TD><TD >7</TD></tr><tr><TD >45 - 49</TD><TD >10</TD></tr><tr><TD >50 - 54</TD><TD >22</TD></tr><tr><TD >55 - 59</TD><TD >15</TD></tr><tr><TD >60 - 64</TD><TD >F2</TD></tr><tr><TD >65 - 69</TD><TD >6</TD></tr><tr><TD >70 - 74</TD><TD >3</TD></tr>\n" );
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document.write( "To find F2, we'll add up each of the frequencies. The total sum is 75<BR>\n" );
document.write( "7+10+22+15+F2+6+3 = 75<BR>\n" );
document.write( "63+F2 = 75<BR>\n" );
document.write( "F2 = 75-63<BR>\n" );
document.write( "F2 = 12\r<BR>\n" );
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document.write( "Here's the full completed grouped frequency table<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Marks</TD><TD >Frequency</TD></tr><tr><TD >40 - 44</TD><TD >7</TD></tr><tr><TD >45 - 49</TD><TD >10</TD></tr><tr><TD >50 - 54</TD><TD >22</TD></tr><tr><TD >55 - 59</TD><TD >15</TD></tr><tr><TD >60 - 64</TD><TD >12</TD></tr><tr><TD >65 - 69</TD><TD >6</TD></tr><tr><TD >70 - 74</TD><TD >3</TD></tr>\n" );
document.write( "</TABLE>You should find that the frequencies sum to 75.\r<BR>\n" );
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document.write( "Deciles split the data set into 10 equal pieces<BR>\n" );
document.write( "The 5th decile is the median point because we're 5/10 = 1/2 of the way there.<BR>\n" );
document.write( "1/2 of 75 = 75/2 = 37.5\r<BR>\n" );
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document.write( "Start at the first frequency (7) and add down until we reach 37.5 or go over.<BR>\n" );
document.write( "7 is too short<BR>\n" );
document.write( "7+10 = 17 is too short also<BR>\n" );
document.write( "7+10+22 = 39 we've gone over the mark of 37.5<BR>\n" );
document.write( "The median is somewhere in the interval from 50 to 54 (when we added on that last frequency of 22)\r<BR>\n" );
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document.write( "Unfortunately we don't have enough info to pinpoint exactly where the 5th decile is. I think an acceptable answer is to state the interval 50 - 54, or to state \"a score between 50 and 54\".\r<BR>\n" );
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document.write( "The 60th percentile is the marker where 60% of the scores are below this value.\r<BR>\n" );
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document.write( "60% of 75 = 0.60*75 = 45<BR>\n" );
document.write( "We see that 45 students are below the 60th percentile person.\r<BR>\n" );
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document.write( "Like before, we'll add up the frequencies until we hit 45 or go over.<BR>\n" );
document.write( "7 is too short<BR>\n" );
document.write( "7+10 = 17 is too short<BR>\n" );
document.write( "7+10+22 = 39 is too short<BR>\n" );
document.write( "7+10+22+15 = 54 goes overboard\r<BR>\n" );
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document.write( "The 60th percentile scorer is somewhere in the interval of 55 to 59.<BR>\n" );
document.write( "Like the previous section, we don't have enough info to pin down the exact score.\r<BR>\n" );
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document.write( "The 1st quartile is equivalent to finding the 25th percentile<BR>\n" );
document.write( "We want to know what marker has 25% of the data below this value.\r<BR>\n" );
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document.write( "25% of 75 = 0.25*75 = 18.75<BR>\n" );
document.write( "We round 18.75 to 19\r<BR>\n" );
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document.write( "About 19 students are below the 25th percentile marker\r<BR>\n" );
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document.write( "We'll use the same trick as the previous sections to try to get to 19 or higher<BR>\n" );
document.write( "7 is too short<BR>\n" );
document.write( "7+10 = 17 is too short<BR>\n" );
document.write( "7+10+22 = 39 goes overboard\r<BR>\n" );
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document.write( "The 25th percentile is in the same group as the 5th decile (aka median). <BR>\n" );
document.write( "That group being the \"between 50 and 54\" scores. <BR>\n" );
document.write( "Like the other sections, we don't have enough info to pin down the exact score.<BR>\n" );
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