document.write( "Question 174301: compute the geometric and harmonic means for the following distribution of annual death rates:
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Algebra.Com's Answer #129248 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
compute the geometric and harmonic means for the following distribution of annual death rates:
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document.write( "You just have to learn some rules about the different kinds of averaging:\r\n" );
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document.write( "You didn't ask about arithmetic mean, but we have to use it\r\n" );
document.write( "to find the harmonic mean.\r\n" );
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document.write( "How to find the arithmetic mean of some numbers:\r\n" );
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document.write( "1. Count them.\r\n" );
document.write( "2. Add them all together.\r\n" );
document.write( "3. Divide the result of 2 by the result of 1.\r\n" );
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document.write( "How to find the geometric mean of some numbers:\r\n" );
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document.write( "1. Count them.\r\n" );
document.write( "2. Multiply them all together.\r\n" );
document.write( "3. Take the root corresponding to 1 of the result of 1.\r\n" );
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document.write( "How to find the harmonic mean of some numbers:\r\n" );
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document.write( "1. Take the reciprocals of all the numbers\r\n" );
document.write( "2. Take the arithmetic mean of the results of 1\r\n" );
document.write( "3. Take the reciprocal of the result of 2.\r\n" );
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document.write( "3.95,4.95,5.95,6.95,7.95,8.95,9.95,10.95,11.95,12.95,13.95\r\n" );
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document.write( "To find the geometric mean:\r\n" );
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document.write( "1. Count them.\r\n" );
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document.write( "There are 11 of them\r\n" );
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document.write( "2. Multiply them all together.\r\n" );
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document.write( "(3.95)(4.95)(5.95)(6.95)(7.95)(8.95)(9.95)(10.95)(11.95)(12.95)(13.95)\r\n" );
document.write( "= 1.353141797 × 1010.\r\n" );
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document.write( "3. Take the root corresponding to 1 of the result of 1.\r\n" );
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document.write( "Since we counted 11 in the first step, we take the 11th root:\r\n" );
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document.write( "----\r\n" );
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document.write( "To find the harmonic means:\r\n" );
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document.write( "1. Take the reciprocals of all the numbers:\r\n" );
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document.write( "\"1%2F3.95\",\"1%2F4.95\",\"1%2F5.95\",\"1%2F6.95\",\"1%2F7.95\",\"1%2F8.95\",\"1%2F9.95\",\"1%2F10.95\",\"1%2F11.95\",\"1%2F12.95\",\"1%2F13.95\"\r\n" );
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document.write( "2. Take the arithmetic mean of the results of 1\r\n" );
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document.write( "To find the arithmetic mean of those numbers:\r\n" );
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document.write( "      1a. Count them.  There are 11\r\n" );
document.write( "      2a. Add them all together. 1.19694482\r\n" );
document.write( "      3a. Divide the result of 2 by the result of 1a.\r\n" );
document.write( "         \"matrix%281%2C5%2C+1.19694482%2C+%22%F7%22%2C+11%2C+%22=%22%2C+0.10881317%29\"  \r\n" );
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document.write( "3. Take the reciprocal of the result of 2.\r\n" );
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document.write( "       \"matrix%281%2C3%2C1%2F0.10881317%2C%22=%22+%2C9.19006442%29\"\r\n" );
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document.write( "Edwin
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