document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193985>Question 1193985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Test Obtained by Selected Grade 10 Students in Statistics<BR>\n" );
document.write( "48 73 57 57 69 88 11 80 82 47<BR>\n" );
document.write( "46 70 49 45 75 81 33 65 38 59<BR>\n" );
document.write( "94 59 62 36 58 69 45 55 58 65<BR>\n" );
document.write( "30 49 73 29 41 53 37 35 61 48<BR>\n" );
document.write( "22 51 56 55 60 37 56 59 57 36<BR>\n" );
document.write( "12 36 50 63 68 30 56 70 53 28<BR>\n" );
document.write( "The Frequency Distribution of the Examination Results of Grade 10 Students<BR>\n" );
document.write( "C.I Tally f <BR>\n" );
document.write( "11-22<BR>\n" );
document.write( "23-34<BR>\n" );
document.write( "34-46<BR>\n" );
document.write( "47-58<BR>\n" );
document.write( "59-70<BR>\n" );
document.write( "71-82<BR>\n" );
document.write( "83-94<BR>\n" );
document.write( "Using the frequency distribution above, determine the following<BR>\n" );
document.write( "11. Size of the class interval<BR>\n" );
document.write( "12. Median class<BR>\n" );
document.write( "13. Modal class<BR>\n" );
document.write( "14. Lower boundary of the median class<BR>\n" );
document.write( "15. Upper boundary of the modal class<BR>\n" );
document.write( "16. Upper limit of the modal class<BR>\n" );
document.write( "17. Class midpoint of the modal class<BR>\n" );
document.write( "18. The number of classes<BR>\n" );
document.write( "19. Less than cumulative before the median class<BR>\n" );
document.write( "20. The frequency of the modal class<BR>\n" );
document.write( "21. fm1<BR>\n" );
document.write( "22. fm2<BR>\n" );
document.write( "23. the mean<BR>\n" );
document.write( "24. the median<BR>\n" );
document.write( "25. the mode </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848538 by </B><A HREF=/tutors/aboutme.mpl?userid=parmen><B>parmen(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=parmen><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=848538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **11. Size of the class interval:** \r<BR>\n" );
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document.write( "* Class Interval = Upper Limit - Lower Limit <BR>\n" );
document.write( "* For the first class: 22 - 11 = 11<BR>\n" );
document.write( "* **Size of the class interval: 11** \r<BR>\n" );
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document.write( "**12. Median class:**\r<BR>\n" );
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document.write( "* Find the total number of students (N): 60<BR>\n" );
document.write( "* Find the median position: (N + 1) / 2 = (60 + 1) / 2 = 30.5 <BR>\n" );
document.write( "* The median class is the class containing the 30.5th observation. <BR>\n" );
document.write( "* Looking at the cumulative frequencies, the median class is **47-58**.\r<BR>\n" );
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document.write( "**13. Modal class:**\r<BR>\n" );
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document.write( "* The modal class is the class with the highest frequency. <BR>\n" );
document.write( "* **Modal class: 47-58** \r<BR>\n" );
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document.write( "**14. Lower boundary of the median class:** <BR>\n" );
document.write( "* Lower boundary = Lower limit - 0.5 <BR>\n" );
document.write( "* Lower boundary of 47-58 = 47 - 0.5 = **46.5**\r<BR>\n" );
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document.write( "**15. Upper boundary of the modal class:**<BR>\n" );
document.write( "* Upper boundary = Upper limit + 0.5 <BR>\n" );
document.write( "* Upper boundary of 47-58 = 58 + 0.5 = **58.5**\r<BR>\n" );
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document.write( "**16. Upper limit of the modal class:**<BR>\n" );
document.write( "* **Upper limit of the modal class: 58**\r<BR>\n" );
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document.write( "**17. Class midpoint of the modal class:**\r<BR>\n" );
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document.write( "* Class midpoint = (Lower limit + Upper limit) / 2<BR>\n" );
document.write( "* Class midpoint of 47-58 = (47 + 58) / 2 = 52.5\r<BR>\n" );
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document.write( "**18. The number of classes:**<BR>\n" );
document.write( "* **Number of classes: 7**\r<BR>\n" );
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document.write( "**19. Less than cumulative before the median class:**\r<BR>\n" );
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document.write( "* Calculate the cumulative frequencies for each class.<BR>\n" );
document.write( "* Less than cumulative before the median class (47-58) is the sum of frequencies of all classes before it. <BR>\n" );
document.write( "* **Less than cumulative before the median class: 23**\r<BR>\n" );
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document.write( "**20. The frequency of the modal class:**\r<BR>\n" );
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document.write( "* **Frequency of the modal class (47-58): 17**\r<BR>\n" );
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document.write( "**21. fm1:**\r<BR>\n" );
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document.write( "* fm1 is the frequency of the class preceding the modal class.<BR>\n" );
document.write( "* **fm1 = 12** (frequency of the 34-46 class)\r<BR>\n" );
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document.write( "**22. fm2:**\r<BR>\n" );
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document.write( "* fm2 is the frequency of the class succeeding the modal class.<BR>\n" );
document.write( "* **fm2 = 10** (frequency of the 59-70 class)\r<BR>\n" );
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document.write( "**23. The mean:**\r<BR>\n" );
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document.write( "* To calculate the mean, you would need the midpoint of each class and their respective frequencies. <BR>\n" );
document.write( "* Use the formula: <BR>\n" );
document.write( "   Mean = Σ(f * x) / Σf <BR>\n" );
document.write( "   where 'f' is the frequency of each class and 'x' is the midpoint of each class.\r<BR>\n" );
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document.write( "**24. The median:**\r<BR>\n" );
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document.write( "* Median = L + [(N/2 - cf) / fm] * c <BR>\n" );
document.write( "   where:<BR>\n" );
document.write( "      L = Lower boundary of the median class <BR>\n" );
document.write( "      N = Total number of observations<BR>\n" );
document.write( "      cf = Cumulative frequency before the median class<BR>\n" );
document.write( "      fm = Frequency of the median class<BR>\n" );
document.write( "      c = Class width\r<BR>\n" );
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document.write( "* Median = 46.5 + [(30.5 - 23) / 17] * 11 <BR>\n" );
document.write( "* Median = 46.5 + [7.5 / 17] * 11 <BR>\n" );
document.write( "* Median ≈ 46.5 + 4.91 <BR>\n" );
document.write( "* **Median ≈ 51.41**\r<BR>\n" );
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document.write( "**25. The mode:**\r<BR>\n" );
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document.write( "* The mode is the midpoint of the modal class.<BR>\n" );
document.write( "* **Mode = 52.5**\r<BR>\n" );
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document.write( "**Note:** \r<BR>\n" );
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document.write( "* This analysis assumes that the data within each class is evenly distributed.<BR>\n" );
document.write( "* For more precise calculations of the mean and other statistics, you would need the original raw data.\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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