document.write( "Question 771309: What is the variance of the set of numbers? Please show work\r
\n" ); document.write( "\n" ); document.write( "16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 30, 30, 31, 32, 32, 32, 33, 34, 34, 34, 34, 34, 33, 35, 35, 35, 35, 35, 36, 36, 37, 37, 38, 38, 39, 40, 41, 42, 42, 42, 42, 42, 43, 44, 45, 46, 48, 49, 51, 53, 55, 55, 56, 58, 60, 62\r
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Algebra.Com's Answer #470157 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You'll have to do it for your long list of data.\r\n" );
document.write( "This one stops at 19, but yours goes to 62.\r\n" );
document.write( "I'm just going to show you how you would do it\r\n" );
document.write( "if there were only the first 4 values in your\r\n" );
document.write( "list. So don't use the sums below.  Do it for\r\n" );
document.write( "you whole list, which will take a long time. \r\n" );
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document.write( "Make this chart.  The frequencies f are how many of that number\r\n" );
document.write( "are in the list. You have 2 16s, 4 17's, 5 18's and 6 19's.\r\n" );
document.write( "Then multiply the f's by the x's. And add up the f's and the\r\n" );
document.write( "f·x's.\r\n" );
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document.write( "x   f  f·x   x-x  (x-x)²  f·(x-x)²\r\n" );
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document.write( "16  2   32   \r\n" );
document.write( "17  4   68 \r\n" );
document.write( "18  5   90\r\n" );
document.write( "19  6  114\r\n" );
document.write( "---------------------------------\r\n" );
document.write( "   17  304\r\n" );
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document.write( "Now divide the ∑f·x = 304 by the ∑f = n = 17 and get x = 17.88\r\n" );
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document.write( "Subtract x = 17.88 from each x and put it in the next column.\r\n" );
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document.write( "x   f  f·x   x-x  (x-x)²  f·(x-x)²\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "16  2   32 -1.88   \r\n" );
document.write( "17  4   68  -.88 \r\n" );
document.write( "18  5   90   .12\r\n" );
document.write( "19  6  114  1.12 \r\n" );
document.write( "---------------------------------\r\n" );
document.write( "   17  304  \r\n" );
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document.write( "We square each number in that column\r\n" );
document.write( "and put it in the next column. \r\n" );
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document.write( "x   f  f·x   x-x  (x-x)²  f·(x-x)²\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "16  2   32 -1.88   3.53   \r\n" );
document.write( "17  4   68  -.88    .77\r\n" );
document.write( "18  5   90   .12   1.44  \r\n" );
document.write( "19  6  114  1.12   1.25 \r\n" );
document.write( "---------------------------------\r\n" );
document.write( "   17  304    \r\n" );
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document.write( "Now we multiply the number in column f times\r\n" );
document.write( "the numbers in column (x-x)² and put those\r\n" );
document.write( "values in the last column.  Add that last column\r\n" );
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document.write( "x   f  f·x   x-x  (x-x)²  f·(x-x)²\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "16  2   32 -1.88   3.54     7.09   \r\n" );
document.write( "17  4   68  -.88    .77     3.11\r\n" );
document.write( "18  5   90   .12    .01      .07     \r\n" );
document.write( "19  6  114  1.12   1.25     7.49  \r\n" );
document.write( "---------------------------------\r\n" );
document.write( "   17  304                 17.76\r\n" );
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document.write( "Now divide that ∑f·(x-x)² by n-1 which is 17-1 or 16,\r\n" );
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document.write( "and you get the variance = s² = 1.11\r\n" );
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document.write( "You'll have to do that will all your data.  It's\r\n" );
document.write( "going to be a lot of work.  And maybe you'll need\r\n" );
document.write( "to take the decimals out further to get the\r\n" );
document.write( "accuracy you need.\r\n" );
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document.write( "Edwin
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