document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200043>Question 1200043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The flowing data is organized by using a stem-and lead displays for the weights of 10 people<BR>\n" );
document.write( "Stems                                                                     Leaves <BR>\n" );
document.write( "5                                                                               0 2<BR>\n" );
document.write( "6                                                                               2 4 4<BR>\n" );
document.write( "7                                                                               1 5 5 5<BR>\n" );
document.write( "8                                                                                8<BR>\n" );
document.write( "Based on the above data:<BR>\n" );
document.write( "a)	Develop the frequency distribution table <BR>\n" );
document.write( "b)	Show on the table the relative frequently distribution and percent frequency distribution for each group <BR>\n" );
document.write( "c)	Calculate the mean <BR>\n" );
document.write( "d)	Calculate 1 percent of trimmed mean <BR>\n" );
document.write( "e)	Calculate the weighted mean <BR>\n" );
document.write( "f)	Calculate median <BR>\n" );
document.write( "g)	Calculate the mode <BR>\n" );
document.write( "h)	Calculate the range <BR>\n" );
document.write( "i)	Find the first, second and third quartile <BR>\n" );
document.write( "j)	Calculate the 80th percentile and interpret the results obtained <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 #848132 by </B><A HREF=/tutors/aboutme.mpl?userid=textot><B>textot(100)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=textot><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=848132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Frequency Distribution Table**\r<BR>\n" );
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document.write( "| Weight (kg) | Frequency (f) |<BR>\n" );
document.write( "|---|---|<BR>\n" );
document.write( "| 50 | 2 |<BR>\n" );
document.write( "| 52 | 1 |<BR>\n" );
document.write( "| 62 | 1 |<BR>\n" );
document.write( "| 64 | 2 |<BR>\n" );
document.write( "| 71 | 1 |<BR>\n" );
document.write( "| 75 | 3 |<BR>\n" );
document.write( "| 88 | 1 |<BR>\n" );
document.write( "| **Total** | **10** |\r<BR>\n" );
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document.write( "**b) Relative and Percent Frequency Distribution**\r<BR>\n" );
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document.write( "| Weight (kg) | Frequency (f) | Relative Frequency (f/n) | Percent Frequency (%) |<BR>\n" );
document.write( "|---|---|---|---|<BR>\n" );
document.write( "| 50 | 2 | 2/10 = 0.20 | 20% |<BR>\n" );
document.write( "| 52 | 1 | 1/10 = 0.10 | 10% |<BR>\n" );
document.write( "| 62 | 1 | 1/10 = 0.10 | 10% |<BR>\n" );
document.write( "| 64 | 2 | 2/10 = 0.20 | 20% |<BR>\n" );
document.write( "| 71 | 1 | 1/10 = 0.10 | 10% |<BR>\n" );
document.write( "| 75 | 3 | 3/10 = 0.30 | 30% |<BR>\n" );
document.write( "| 88 | 1 | 1/10 = 0.10 | 10% |<BR>\n" );
document.write( "| **Total** | **10** | **1.00** | **100%** |\r<BR>\n" );
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document.write( "**c) Mean**\r<BR>\n" );
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document.write( "* **Calculate the sum of all weights:** <BR>\n" );
document.write( "   * 50 + 52 + 62 + 64 + 64 + 71 + 75 + 75 + 75 + 88 = 672 <BR>\n" );
document.write( "* **Divide the sum of weights by the number of observations (n = 10):**<BR>\n" );
document.write( "   * Mean = 672 / 10 = **67.2 kg**\r<BR>\n" );
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document.write( "**d) 1% Trimmed Mean**\r<BR>\n" );
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document.write( "* **Remove 1% of data from both ends:** <BR>\n" );
document.write( "   * Remove the lowest weight (50 kg) and the highest weight (88 kg).<BR>\n" );
document.write( "* **Calculate the mean of the remaining 8 values:**<BR>\n" );
document.write( "   * Sum of remaining weights: 52 + 62 + 64 + 64 + 71 + 75 + 75 + 75 = 533<BR>\n" );
document.write( "   * Trimmed Mean = 533 / 8 = **66.625 kg**\r<BR>\n" );
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document.write( "**e) Weighted Mean (Not applicable in this case)**\r<BR>\n" );
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document.write( "* A weighted mean is used when different data points have different weights or importance. Since all weights in this dataset have equal importance, a simple mean is sufficient.\r<BR>\n" );
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document.write( "**f) Median**\r<BR>\n" );
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document.write( "* **Arrange the data in ascending order:** <BR>\n" );
document.write( "   * 50, 52, 62, 64, 64, 71, 75, 75, 75, 88<BR>\n" );
document.write( "* **Find the middle value:** <BR>\n" );
document.write( "   * Since there are 10 observations (an even number), the median is the average of the 5th and 6th values:<BR>\n" );
document.write( "      * Median = (64 + 71) / 2 = **67.5 kg**\r<BR>\n" );
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document.write( "**g) Mode**\r<BR>\n" );
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document.write( "* **The mode is the most frequent value:**<BR>\n" );
document.write( "   * **Mode = 75 kg** (occurs 3 times)\r<BR>\n" );
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document.write( "**h) Range**\r<BR>\n" );
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document.write( "* **Range = Maximum value - Minimum value**<BR>\n" );
document.write( "   * Range = 88 kg - 50 kg = **38 kg**\r<BR>\n" );
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document.write( "**i) Quartiles**\r<BR>\n" );
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document.write( "* **First Quartile (Q1):** <BR>\n" );
document.write( "   * Median of the lower half of the data (excluding the median if the number of data points is odd).<BR>\n" );
document.write( "      * Lower half: 50, 52, 62, 64, 64 <BR>\n" );
document.write( "      * Q1 = 62 kg<BR>\n" );
document.write( "* **Second Quartile (Q2):** <BR>\n" );
document.write( "   * Median of the data (already calculated) <BR>\n" );
document.write( "      * Q2 = 67.5 kg<BR>\n" );
document.write( "* **Third Quartile (Q3):** <BR>\n" );
document.write( "   * Median of the upper half of the data (excluding the median if the number of data points is odd).<BR>\n" );
document.write( "      * Upper half: 71, 75, 75, 75, 88 <BR>\n" );
document.write( "      * Q3 = 75 kg\r<BR>\n" );
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document.write( "**j) 80th Percentile**\r<BR>\n" );
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document.write( "* **The 80th percentile is the value below which 80% of the data falls.**<BR>\n" );
document.write( "* **Find the position of the 80th percentile:** <BR>\n" );
document.write( "   * Position = (80/100) * n = 0.80 * 10 = 8th position<BR>\n" );
document.write( "* **The 80th percentile is the 8th value in the ordered data:**<BR>\n" );
document.write( "   * 80th percentile = 75 kg\r<BR>\n" );
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document.write( "**Interpretation of 80th Percentile:** <BR>\n" );
document.write( "80% of the people in the sample weigh 75 kg or less.<BR>\n" );
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