document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179330>Question 1179330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SCORES<BR>\n" );
document.write( "46-50<BR>\n" );
document.write( "41-45<BR>\n" );
document.write( "36-40<BR>\n" );
document.write( "31-35<BR>\n" );
document.write( "26-30<BR>\n" );
document.write( "21-25\r<BR>\n" );
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document.write( "FREQUENCY<BR>\n" );
document.write( "5<BR>\n" );
document.write( "11<BR>\n" );
document.write( "8<BR>\n" );
document.write( "16<BR>\n" );
document.write( "3<BR>\n" );
document.write( "7\r<BR>\n" );
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document.write( "A. Calculate the 1st quartile<BR>\n" );
document.write( "b. \" 2nd quartile<BR>\n" );
document.write( "c. \" 3rd quartile<BR>\n" );
document.write( "d. \" 7th decile<BR>\n" );
document.write( "e. \" 3rd decile<BR>\n" );
document.write( "f. \" 25th percentile<BR>\n" );
document.write( "g. \" 60th percentile\r<BR>\n" );
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document.write( "I tried to solve this but, my answers were not correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850245 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=850245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's calculate the quartiles, deciles, and percentiles for the given grouped frequency distribution.\r<BR>\n" );
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document.write( "1. Calculate Cumulative Frequencies:\r<BR>\n" );
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document.write( "Scores	Frequency	Cumulative Frequency<BR>\n" );
document.write( "46-50	5	5<BR>\n" );
document.write( "41-45	11	16<BR>\n" );
document.write( "36-40	8	24<BR>\n" );
document.write( "31-35	16	40<BR>\n" );
document.write( "26-30	3	43<BR>\n" );
document.write( "21-25	7	50\r<BR>\n" );
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document.write( "Export to Sheets<BR>\n" );
document.write( "Total frequency (n) = 50\r<BR>\n" );
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document.write( "2. Calculate Quartiles:\r<BR>\n" );
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document.write( "Q1 (1st Quartile):\r<BR>\n" );
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document.write( "Position of Q1 = (1/4) * n = (1/4) * 50 = 12.5<BR>\n" );
document.write( "12.5 falls in the 41-45 bin (cumulative frequency 16).<BR>\n" );
document.write( "Lower boundary (L) = 40.5<BR>\n" );
document.write( "Class width (w) = 5<BR>\n" );
document.write( "Frequency of Q1 class (f) = 11<BR>\n" );
document.write( "Cumulative frequency before Q1 class (cf) = 5<BR>\n" );
document.write( "Q1 = L + [(12.5 - cf) / f] * w = 40.5 + [(12.5 - 5) / 11] * 5 = 40.5 + (7.5 / 11) * 5 ≈ 40.5 + 3.41 ≈ 43.91<BR>\n" );
document.write( "Q2 (2nd Quartile/Median):\r<BR>\n" );
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document.write( "Position of Q2 = (2/4) * n = (1/2) * 50 = 25<BR>\n" );
document.write( "25 falls in the 31-35 bin (cumulative frequency 40).<BR>\n" );
document.write( "Lower boundary (L) = 30.5<BR>\n" );
document.write( "Class width (w) = 5<BR>\n" );
document.write( "Frequency of Q2 class (f) = 16<BR>\n" );
document.write( "Cumulative frequency before Q2 class (cf) = 24<BR>\n" );
document.write( "Q2 = L + [(25 - cf) / f] * w = 30.5 + [(25 - 24) / 16] * 5 = 30.5 + (1 / 16) * 5 ≈ 30.5 + 0.31 ≈ 30.81<BR>\n" );
document.write( "Q3 (3rd Quartile):\r<BR>\n" );
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document.write( "Position of Q3 = (3/4) * n = (3/4) * 50 = 37.5<BR>\n" );
document.write( "37.5 falls in the 31-35 bin (cumulative frequency 40).<BR>\n" );
document.write( "Lower boundary (L) = 30.5<BR>\n" );
document.write( "Class width (w) = 5<BR>\n" );
document.write( "Frequency of Q3 class (f) = 16<BR>\n" );
document.write( "Cumulative frequency before Q3 class (cf) = 24<BR>\n" );
document.write( "Q3 = L + [(37.5 - cf) / f] * w = 30.5 + [(37.5 - 24) / 16] * 5 = 30.5 + (13.5 / 16) * 5 ≈ 30.5 + 4.22 ≈ 34.72<BR>\n" );
document.write( "3. Calculate Deciles:\r<BR>\n" );
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document.write( "D7 (7th Decile):\r<BR>\n" );
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document.write( "Position of D7 = (7/10) * n = (7/10) * 50 = 35<BR>\n" );
document.write( "35 falls in the 31-35 bin (cumulative frequency 40).<BR>\n" );
document.write( "Lower boundary (L) = 30.5<BR>\n" );
document.write( "Class width (w) = 5<BR>\n" );
document.write( "Frequency of D7 class (f) = 16<BR>\n" );
document.write( "Cumulative frequency before D7 class (cf) = 24<BR>\n" );
document.write( "D7 = L + [(35 - cf) / f] * w = 30.5 + [(35 - 24) / 16] * 5 = 30.5 + (11 / 16) * 5 ≈ 30.5 + 3.44 ≈ 33.94<BR>\n" );
document.write( "D3 (3rd Decile):\r<BR>\n" );
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document.write( "Position of D3 = (3/10) * n = (3/10) * 50 = 15<BR>\n" );
document.write( "15 falls in the 41-45 bin (cumulative frequency 16).<BR>\n" );
document.write( "Lower boundary (L) = 40.5<BR>\n" );
document.write( "Class width (w) = 5<BR>\n" );
document.write( "Frequency of D3 class (f) = 11<BR>\n" );
document.write( "Cumulative frequency before D3 class (cf) = 5<BR>\n" );
document.write( "D3 = L + [(15 - cf) / f] * w = 40.5 + [(15 - 5) / 11] * 5 = 40.5 + (10 / 11) * 5 ≈ 40.5 + 4.55 ≈ 45.05<BR>\n" );
document.write( "4. Calculate Percentiles:\r<BR>\n" );
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document.write( "P25 (25th Percentile):\r<BR>\n" );
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document.write( "Same as Q1. P25 ≈ 43.91<BR>\n" );
document.write( "P60 (60th Percentile):\r<BR>\n" );
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document.write( "Position of P60 = (60/100) * n = (60/100) * 50 = 30<BR>\n" );
document.write( "30 falls in the 31-35 bin (cumulative frequency 40).<BR>\n" );
document.write( "Lower boundary (L) = 30.5<BR>\n" );
document.write( "Class width (w) = 5<BR>\n" );
document.write( "Frequency of P60 class (f) = 16<BR>\n" );
document.write( "Cumulative frequency before P60 class (cf) = 24<BR>\n" );
document.write( "P60 = L + [(30 - cf) / f] * w = 30.5 + [(30 - 24) / 16] * 5 = 30.5 + (6 / 16) * 5 ≈ 30.5 + 1.88 ≈ 32.38<BR>\n" );
document.write( "Answers (rounded to two decimal places):\r<BR>\n" );
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document.write( "a. Q1 ≈ 43.91<BR>\n" );
document.write( "b. Q2 ≈ 30.81<BR>\n" );
document.write( "c. Q3 ≈ 34.72<BR>\n" );
document.write( "d. D7 ≈ 33.94<BR>\n" );
document.write( "e. D3 ≈ 45.05<BR>\n" );
document.write( "f. P25 ≈ 43.91<BR>\n" );
document.write( "g. P60 ≈ 32.38 </SPAN>\n" );
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