document.write( "Question 577228: The ages of 10 students are listed in years:{ 17,22,19,24,21,23,29,18,22,28 }
\n" ); document.write( "(a) Find the mean, median, mode, sample variance, and range.
\n" ); document.write( "(b) Do you think that this sample might have come from a normal population? Why or why not? \n" ); document.write( "
Algebra.Com's Answer #370135 by Edwin McCravy(20055)\"\" \"About 
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17,22,19,24,21,23,29,18,22,28
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document.write( "First we arrange them in a column headed x.  Add the column,\r\n" );
document.write( "and divide by the number of values, which is 10\r\n" );
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document.write( "     x\r\n" );
document.write( "    17\r\n" );
document.write( "    18\r\n" );
document.write( "    19\r\n" );
document.write( "    21\r\n" );
document.write( "    22\r\n" );
document.write( "    22\r\n" );
document.write( "    23\r\n" );
document.write( "    24\r\n" );
document.write( "    28\r\n" );
document.write( "    29\r\n" );
document.write( "  ______\r\n" );
document.write( "10)223.0\r\n" );
document.write( "    22.3\r\n" );
document.write( "   _\r\n" );
document.write( "So x = 22.3 = the mean. \r\n" );
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document.write( "To find the median, we average the two numbers in the middle when\r\n" );
document.write( "they are arranged from smallest to largest.  The two numbers in\r\n" );
document.write( "the middle are 22 and 22, and their average is 22, so the median\r\n" );
document.write( "is 22.\r\n" );
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document.write( "The number occurring the most number of times is the mode.  22\r\n" );
document.write( "occurs twice in the column, so the mode is 22.\r\n" );
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document.write( "To find the sample variance, out beside that column we write\r\n" );
document.write( "a second column headed \r\n" );
document.write( "  _\r\n" );
document.write( "x-x and the numbers in that bar are the numbers in the x column with\r\n" );
document.write( "the mean 22.3 subtracted from them\r\n" );
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document.write( "            _ \r\n" );
document.write( "     x    x-x\r\n" );
document.write( "    17   -5.3\r\n" );
document.write( "    18   -4.3\r\n" );
document.write( "    19   -3.3\r\n" );
document.write( "    21   -1.3\r\n" );
document.write( "    22   -0.3\r\n" );
document.write( "    22   -0.3\r\n" );
document.write( "    23    0.7\r\n" );
document.write( "    24    1.7\r\n" );
document.write( "    28    5.7\r\n" );
document.write( "    29    6.7\r\n" );
document.write( "  ______\r\n" );
document.write( "10)223.0\r\n" );
document.write( "    22.3\r\n" );
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document.write( "Out beside that column we make a thrid column of squaring the number\r\n" );
document.write( "in the column and we head it:\r\n" );
document.write( "   _\r\n" );
document.write( "(x-x)²\r\n" );
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document.write( "We add that column and divide by 1 less than the number of\r\n" );
document.write( "values, which means we divide by 10-1 or 9:\r\n" );
document.write( "            _ \r\n" );
document.write( "     x    x-x   (x-x)²\r\n" );
document.write( "    17   -5.3   28.09\r\n" );
document.write( "    18   -4.3   18.49\r\n" );
document.write( "    19   -3.3   10.89\r\n" );
document.write( "    21   -1.3    1.69\r\n" );
document.write( "    22   -0.3    0.09\r\n" );
document.write( "    22   -0.3    0.09\r\n" );
document.write( "    23    0.7    0.49\r\n" );
document.write( "    24    1.7    2.89\r\n" );
document.write( "    28    5.7   32.49 \r\n" );
document.write( "    29    6.7   44.89\r\n" );
document.write( "  ______      _______\r\n" );
document.write( "10)223.0     9)140.10\r\n" );
document.write( "    22.3        15.56666... round to 15.57\r\n" );
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document.write( "The variance is 15.57\r\n" );
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document.write( "It is not normally distributed because there is only\r\n" );
document.write( "1 of each data value except 22.  If you draw a histogram \r\n" );
document.write( "of the data it is not mound-shaped at all.\r\n" );
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document.write( "Edwin
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