Question 1086906
...a set of five positive integers. 
<pre>
Suppose the five positive integers are a,b,c,d,e where

a &#8804; b &#8804; c &#8804; d &#8804; e, ascending order.
</pre>
11 is both the median and the mode... 
<pre>
Since 11 is the median and the number of positive 
integers is 5, an odd number, the middle integer,
c = 11.  So,

a &#8804; b &#8804; 11 &#8804; d &#8804; e
</pre>
What is the least possible value of the average (arithmetic mean) of 
the set?
<pre>
We want the arithmetic mean (average) to be as small as 
possible, so we want to use the smallest positive
integers as possible.  The smallest we can take d and e 
to be is 11 each.  Then 11 will also be the mode, which 
is what we want.  Then the smallest that a and b can be 
is 1 each, So we have 

1 &#8804; 1 &#8804; 11 &#8804; 11 &#8804; 11

The least possible average is {{{matrix(1,5,(1+1+11+11+11)/5,""="",35/5,""="",7)}}} 

Edwin</pre>