document.write( "Question 1195524: 3. The frequency distribution of the weights of 60 pieces of luggage, recorded to the nearest kilogram, belonging to the passengers on a flight from Manila to Cebu is shown below:
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\n" ); document.write( "7-9 2
\n" ); document.write( "10-12 8
\n" ); document.write( "13-15 10
\n" ); document.write( "16-18 17
\n" ); document.write( "19-21 23
\n" ); document.write( "22-24 3
\n" ); document.write( "Calculate the range and the mean.
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Algebra.Com's Answer #828064 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "The frequency distribution of the weights of 60 pieces of luggage, recorded to the nearest kilogram, belonging to the passengers on a flight from Manila to Cebu is shown below:
\n" ); document.write( "Weight (kilograms) Pieces
\n" ); document.write( "7-9 2
\n" ); document.write( "10-12 8
\n" ); document.write( "13-15 10
\n" ); document.write( "16-18 17
\n" ); document.write( "19-21 23
\n" ); document.write( "22-24 3
\n" ); document.write( "Calculate the range and the mean.
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document.write( "To calculate the range, we should determine its lower boundary and its upper boundary.\r\n" );
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document.write( "To calculate the lower boundary, in the column \"Weight\" take smallest values,\r\n" );
document.write( "multiply each such value by the factor \"Pieces\" and add all such products over all \r\n" );
document.write( "the rows of the table\r\n" );
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document.write( "    lower boundary = 7*2 + 10*8 + 13*10 + 16*17 + 19*23 + 22*3.   Use your calculator.\r\n" );
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document.write( "To calculate the upper boundary, in the column \"Weight\" take greatest values,\r\n" );
document.write( "multiply each such value by the factor \"Pieces\" and add all such products over all \r\n" );
document.write( "the rows of the table\r\n" );
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document.write( "    upper boundary = 9*2 + 12*8 + 15*10 + 18*17 + 21*23 + 24*3.   Use your calculator.\r\n" );
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document.write( "Thus the range is this interval  [lower boundary, upper boundary].\r\n" );
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document.write( "    +---------------------------------------------------------+\r\n" );
document.write( "    |    Regarding the mean, the problem does not determine   |\r\n" );
document.write( "    |      WHICH mean it wants to compute, UNFORTUNATELY,     |\r\n" );
document.write( "    |        which is a BIG FAULT for a Math problem.         |\r\n" );
document.write( "    +---------------------------------------------------------+\r\n" );
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document.write( "In this problem, there are TWO meaningful conceptions of the \"mean\".\r\n" );
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document.write( "One conception of the mean is \"total mean weight\". \r\n" );
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document.write( "It is the arithmetic mean of the lower and upper range values\r\n" );
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document.write( "    mean as the \"mean total weight\" = .\r\n" );
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document.write( "Another conception of the mean is \"mean weight per single item\". \r\n" );
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document.write( "It is the mean total weight divided by the total number of items/(pieces)\r\n" );
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document.write( "    mean as the \"mean weight per single item\" = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, I complete my explanations.\r
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