document.write( "Question 1086906: 11 is both the median and the mode of a set of five positive integers.
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Algebra.Com's Answer #701152 by Edwin McCravy(20060) $\"\"$ $\"About$

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...a set of five positive integers.
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document.write( "Suppose the five positive integers are a,b,c,d,e where\r\n" );
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document.write( "a ≤ b ≤ c ≤ d ≤ e, ascending order.\r\n" );
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\n" ); document.write( "11 is both the median and the mode...
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document.write( "Since 11 is the median and the number of positive \r\n" );
document.write( "integers is 5, an odd number, the middle integer,\r\n" );
document.write( "c = 11.  So,\r\n" );
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document.write( "a ≤ b ≤ 11 ≤ d ≤ e\r\n" );
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\n" ); document.write( "What is the least possible value of the average (arithmetic mean) of
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document.write( "We want the arithmetic mean (average) to be as small as \r\n" );
document.write( "possible, so we want to use the smallest positive\r\n" );
document.write( "integers as possible.  The smallest we can take d and e \r\n" );
document.write( "to be is 11 each.  Then 11 will also be the mode, which \r\n" );
document.write( "is what we want.  Then the smallest that a and b can be \r\n" );
document.write( "is 1 each, So we have \r\n" );
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document.write( "1 ≤ 1 ≤ 11 ≤ 11 ≤ 11\r\n" );
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document.write( "The least possible average is  \r\n" );
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document.write( "Edwin

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