document.write( "Question 1036440: How do I find the variance and the standard deviation in this problem?
\n" ); document.write( "I know the range is 11 and the mean is 16.2..\r
\n" ); document.write( "\n" ); document.write( "The ages (in years) of a random sample of shoppers at a gaming store are shown. determine the range, mean, variance, and standard deviation of the sample data set.\r
\n" ); document.write( "\n" ); document.write( "12, 17, 23, 13, 14, 17, 20, 16, 15, 15\r
\n" ); document.write( "\n" ); document.write( "The variance is...\r
\n" ); document.write( "\n" ); document.write( "The standard deviation is... \n" ); document.write( "
Algebra.Com's Answer #651104 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here's what to do with a list of data.  \r\n" );
document.write( "Start with this column of x values, add\r\n" );
document.write( "and divide by the number of numbers to\r\n" );
document.write( "get the mean, x.\r\n" );
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document.write( "     x \r\n" );
document.write( "    12 \r\n" );
document.write( "    17 \r\n" );
document.write( "    23 \r\n" );
document.write( "    13\r\n" );
document.write( "    14\r\n" );
document.write( "    17\r\n" );
document.write( "    20\r\n" );
document.write( "    16 \r\n" );
document.write( "    15\r\n" );
document.write( "    15\r\n" );
document.write( "  -----\r\n" );
document.write( "10)162.0 \r\n" );
document.write( "x = 16.2\r\n" );
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document.write( "Then you make another column where you subtract x = 16.2 from\r\n" );
document.write( "each number in the x-column.\r\n" );
document.write( "That column is labeled x-x\r\n" );
document.write( "There is no use to add it, because if you do \r\n" );
document.write( "you will just get 0\r\n" );
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document.write( "     x       x-x       \r\n" );
document.write( "    12      -4.2      \r\n" );
document.write( "    17       0.8       \r\n" );
document.write( "    23       6.8      \r\n" );
document.write( "    13      -3.2      \r\n" );
document.write( "    14      -2.2       \r\n" );
document.write( "    17       0.8       \r\n" );
document.write( "    20       3.8      \r\n" );
document.write( "    16      -0.2      \r\n" );
document.write( "    15      -1.2       \r\n" );
document.write( "    15      -1.2       \r\n" );
document.write( "  -----    -----           \r\n" );
document.write( "10)162.0     0.0       \r\n" );
document.write( "x = 16.2\r\n" );
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document.write( "We square each number in that column and\r\n" );
document.write( "put those squares in a new column.  We\r\n" );
document.write( "add them and divide by 1 less than the\r\n" );
document.write( "number of numbers.           \r\n" );
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document.write( "     x       x-x      (x-x)²\r\n" );
document.write( "----------------------------- \r\n" );
document.write( "    12      -4.2      17.64\r\n" );
document.write( "    17       0.8       0.64\r\n" );
document.write( "    23       6.8      46.24\r\n" );
document.write( "    13      -3.2      10.24\r\n" );
document.write( "    14      -2.2       4.84\r\n" );
document.write( "    17       0.8       0.64\r\n" );
document.write( "    20       3.8      14.44\r\n" );
document.write( "    16      -0.2       0.04\r\n" );
document.write( "    15      -1.2       1.44\r\n" );
document.write( "    15      -1.2       1.44\r\n" );
document.write( "  -----    -----      -----\r\n" );
document.write( "10)162.0     0.0     9)97.60\r\n" );
document.write( "x = 16.2            s²=10.8444...\r\n" );
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document.write( "The sample variance is 10.8444...\r\n" );
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document.write( "The sample standard deviation is the square root of\r\n" );
document.write( "the variance, s = 3.293090409...\r\n" );
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document.write( "Edwin
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