document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176858>Question 1176858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the appropriate formula to find the quartiles of the following,do not forget to state your interpretations:<BR>\n" );
document.write( "Raw scores of 48 students in a mathematics 8 test<BR>\n" );
document.write( "SCORES: f: lb: cumulative frequency cf:<BR>\n" );
document.write( "46-50  1  45.5  48<BR>\n" );
document.write( "41-45  5  40.5  47<BR>\n" );
document.write( "36-40  11 35.5  42<BR>\n" );
document.write( "31-35  12 30.5  31<BR>\n" );
document.write( "26-30  11 25.5  19<BR>\n" );
document.write( "21-25  5  20.5  8<BR>\n" );
document.write( "16-20  2  15.5  3<BR>\n" );
document.write( "11-15  1  10.5  1<BR>\n" );
document.write( "____Σr = 48 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850559 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=850559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's find the quartiles for the given grouped data and interpret the results.\r<BR>\n" );
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document.write( "**1. Understanding Quartiles**\r<BR>\n" );
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document.write( "* **Q1 (First Quartile):** The value below which 25% of the data falls.<BR>\n" );
document.write( "* **Q2 (Second Quartile):** The median, the value below which 50% of the data falls.<BR>\n" );
document.write( "* **Q3 (Third Quartile):** The value below which 75% of the data falls.\r<BR>\n" );
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document.write( "**2. Formulas for Grouped Data**\r<BR>\n" );
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document.write( "The formula for finding quartiles in grouped data is:\r<BR>\n" );
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document.write( "* Qk = L + [(kN/4 - cf) / f] * w\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* Qk = the kth quartile<BR>\n" );
document.write( "* L = lower boundary of the quartile class<BR>\n" );
document.write( "* N = total number of data points<BR>\n" );
document.write( "* cf = cumulative frequency of the class before the quartile class<BR>\n" );
document.write( "* f = frequency of the quartile class<BR>\n" );
document.write( "* w = class width\r<BR>\n" );
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document.write( "**3. Calculate Quartiles**\r<BR>\n" );
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document.write( "* N = 48<BR>\n" );
document.write( "* Class width (w) = 5 (e.g., 50 - 46 + 1 = 5)\r<BR>\n" );
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document.write( "**a) Q1 (First Quartile)**\r<BR>\n" );
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document.write( "* kN/4 = (1 * 48) / 4 = 12<BR>\n" );
document.write( "* The 12th value falls in the 26-30 class (cf = 19, which is > 12).<BR>\n" );
document.write( "* L = 25.5<BR>\n" );
document.write( "* cf = 8<BR>\n" );
document.write( "* f = 11\r<BR>\n" );
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document.write( "* Q1 = 25.5 + [(12 - 8) / 11] * 5<BR>\n" );
document.write( "* Q1 = 25.5 + (4 / 11) * 5<BR>\n" );
document.write( "* Q1 = 25.5 + 20 / 11<BR>\n" );
document.write( "* Q1 = 25.5 + 1.818<BR>\n" );
document.write( "* Q1 ≈ 27.32\r<BR>\n" );
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document.write( "**b) Q2 (Second Quartile)**\r<BR>\n" );
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document.write( "* kN/4 = (2 * 48) / 4 = 24<BR>\n" );
document.write( "* The 24th value falls in the 31-35 class (cf = 31, which is > 24).<BR>\n" );
document.write( "* L = 30.5<BR>\n" );
document.write( "* cf = 19<BR>\n" );
document.write( "* f = 12\r<BR>\n" );
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document.write( "* Q2 = 30.5 + [(24 - 19) / 12] * 5<BR>\n" );
document.write( "* Q2 = 30.5 + (5 / 12) * 5<BR>\n" );
document.write( "* Q2 = 30.5 + 25 / 12<BR>\n" );
document.write( "* Q2 = 30.5 + 2.083<BR>\n" );
document.write( "* Q2 ≈ 32.58\r<BR>\n" );
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document.write( "**c) Q3 (Third Quartile)**\r<BR>\n" );
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document.write( "* kN/4 = (3 * 48) / 4 = 36<BR>\n" );
document.write( "* The 36th value falls in the 36-40 class (cf = 42, which is > 36).<BR>\n" );
document.write( "* L = 35.5<BR>\n" );
document.write( "* cf = 31<BR>\n" );
document.write( "* f = 11\r<BR>\n" );
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document.write( "* Q3 = 35.5 + [(36 - 31) / 11] * 5<BR>\n" );
document.write( "* Q3 = 35.5 + (5 / 11) * 5<BR>\n" );
document.write( "* Q3 = 35.5 + 25 / 11<BR>\n" );
document.write( "* Q3 = 35.5 + 2.273<BR>\n" );
document.write( "* Q3 ≈ 37.77\r<BR>\n" );
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document.write( "**4. Interpretations**\r<BR>\n" );
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document.write( "* **Q1 ≈ 27.32:** Approximately 25% of the students scored 27.32 or below on the mathematics test.<BR>\n" );
document.write( "* **Q2 ≈ 32.58:** Approximately 50% of the students scored 32.58 or below on the mathematics test. This is also the median score.<BR>\n" );
document.write( "* **Q3 ≈ 37.77:** Approximately 75% of the students scored 37.77 or below on the mathematics test.\r<BR>\n" );
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document.write( "**Summary**\r<BR>\n" );
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document.write( "* Q1 ≈ 27.32<BR>\n" );
document.write( "* Q2 ≈ 32.58<BR>\n" );
document.write( "* Q3 ≈ 37.77<BR>\n" );
document.write( " </SPAN>\n" );
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