document.write( "Question 617183: find the variance, and standard deviation for the following set of scores:\r
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Algebra.Com's Answer #388197 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
find the variance, and standard deviation for the following set of scores:
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document.write( "Add them.\r\n" );
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document.write( "   X                                         \r\n" );
document.write( "   4                                      \r\n" );
document.write( "   2                                      \r\n" );
document.write( "   2                                      \r\n" );
document.write( "   3                                      \r\n" );
document.write( "   5\r\n" );
document.write( "   6\r\n" );
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document.write( "  22\r\n" );
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document.write( "Out beside that column square every number, that is, multiply\r\n" );
document.write( "it by itself, then add that column and you have:\r\n" );
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document.write( "     X      X²                                         \r\n" );
document.write( "     4      16                                   \r\n" );
document.write( "     2       4                                  \r\n" );
document.write( "     2       4                                  \r\n" );
document.write( "     3       9                                  \r\n" );
document.write( "     5      25\r\n" );
document.write( "     6      36 \r\n" );
document.write( "   ---     --- \r\n" );
document.write( " ∑x=22  ∑x²=94\r\n" );
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document.write( "The variance is s².  The short-cut formula is:\r\n" );
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document.write( "     n(∑X²) − (∑X)²\r\n" );
document.write( "s² = --------------\r\n" );
document.write( "       n(n − 1)\r\n" );
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document.write( "We substitute  ∑x=22,  ∑x²=94, and n=6 (the number of numbers)\r\n" );
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document.write( "     6(94) − (22)²\r\n" );
document.write( "s² = -------------- \r\n" );
document.write( "       6(6 − 1)\r\n" );
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document.write( "      564 − 484\r\n" );
document.write( "s² = -------------- \r\n" );
document.write( "         6(5)\r\n" );
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document.write( "          80\r\n" );
document.write( "s² = -------------- \r\n" );
document.write( "          30\r\n" );
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document.write( "s² =  = 2.66666666667\r\n" );
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document.write( "That's the variance.\r\n" );
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document.write( "To get the standard deviation, take the square root:\r\n" );
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document.write( "s =  =  = 1.632993162\r\n" );
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document.write( "Round off all answers to the nearest hundredth.\r\n" );
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document.write( "s² = 2.67\r\n" );
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document.write( " s = 1.63\r\n" );
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document.write( "Edwin

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