document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176041>Question 1176041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the appropriate formula to find the mean,The madian,and the mode of each grouped data.<BR>\n" );
document.write( "scores:                    Frequency:<BR>\n" );
document.write( "46-50.                           2<BR>\n" );
document.write( "41-45.                           9<BR>\n" );
document.write( "36-40.                          10<BR>\n" );
document.write( "31-35.                          14<BR>\n" );
document.write( "26-30.                          10<BR>\n" );
document.write( "21-25.                           5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850596 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=850596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Midpoints**\r<BR>\n" );
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document.write( "* Find the midpoint of each class interval:<BR>\n" );
document.write( "    * 46-50: (46 + 50) / 2 = 48<BR>\n" );
document.write( "    * 41-45: (41 + 45) / 2 = 43<BR>\n" );
document.write( "    * 36-40: (36 + 40) / 2 = 38<BR>\n" );
document.write( "    * 31-35: (31 + 35) / 2 = 33<BR>\n" );
document.write( "    * 26-30: (26 + 30) / 2 = 28\r<BR>\n" );
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document.write( "**2. Mean**\r<BR>\n" );
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document.write( "* Use the formula:<BR>\n" );
document.write( "    * Mean (x̄) = Σ(midpoint * frequency) / Σfrequency<BR>\n" );
document.write( "* x̄ = [(48 * 2) + (43 * 9) + (38 * 10) + (33 * 14) + (28 * 10)] / (2 + 9 + 10 + 14 + 10)<BR>\n" );
document.write( "* x̄ = (96 + 387 + 380 + 462 + 280) / 45<BR>\n" );
document.write( "* x̄ = 1605 / 45<BR>\n" );
document.write( "* x̄ ≈ 35.67\r<BR>\n" );
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document.write( "**3. Median**\r<BR>\n" );
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document.write( "1.  **Find the Cumulative Frequencies:**<BR>\n" );
document.write( "    * 46-50: 2<BR>\n" );
document.write( "    * 41-45: 2 + 9 = 11<BR>\n" );
document.write( "    * 36-40: 11 + 10 = 21<BR>\n" );
document.write( "    * 31-35: 21 + 14 = 35<BR>\n" );
document.write( "    * 26-30: 35 + 10 = 45\r<BR>\n" );
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document.write( "2.  **Identify the Median Class:**<BR>\n" );
document.write( "    * The total number of scores (N) is 45.<BR>\n" );
document.write( "    * The median class is the class where the cumulative frequency is greater than or equal to N/2 (which is 22.5 in this case).<BR>\n" );
document.write( "    * The median class is 31-35.\r<BR>\n" );
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document.write( "3.  **Calculate the Median:**<BR>\n" );
document.write( "    * Use the formula:<BR>\n" );
document.write( "        * Median = L + [(N/2 - cf) / f] * w<BR>\n" );
document.write( "    * Where:<BR>\n" );
document.write( "        * L = Lower boundary of the median class (30.5)<BR>\n" );
document.write( "        * N = Total number of scores (45)<BR>\n" );
document.write( "        * cf = Cumulative frequency of the class before the median class (21)<BR>\n" );
document.write( "        * f = Frequency of the median class (14)<BR>\n" );
document.write( "        * w = Class width (5)<BR>\n" );
document.write( "    * Median = 30.5 + [(22.5 - 21) / 14] * 5<BR>\n" );
document.write( "    * Median = 30.5 + (1.5 / 14) * 5<BR>\n" );
document.write( "    * Median ≈ 31.04\r<BR>\n" );
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document.write( "**4. Mode**\r<BR>\n" );
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document.write( "* The modal class is the class with the highest frequency.<BR>\n" );
document.write( "* In this case, the modal class is 31-35.\r<BR>\n" );
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document.write( "**Summary**\r<BR>\n" );
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document.write( "* Mean: 35.67<BR>\n" );
document.write( "* Median: 31.04<BR>\n" );
document.write( "* Mode: 31-35 </SPAN>\n" );
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