<p><span style="color:#27ae60;"><span style="font-size:20px;">Solving The Problem</span></span></p>
<p>Let's go <span style="color:#8e44ad;"><strong>Piece by Piece</strong></span>, reading slowly and making deductions:</p>
<blockquote>
<p>The average (arithmetic mean) of the II numbers in a list is 14.</p>
</blockquote>
<p>We know about the following relationship between mean and sum: $sum = mean * \#\,values$</p>
<p>Since we know the mean and the number of values, let's work out the sum of this list:</p>
<ul>
<li>$sum = 14 * 11$</li>
<li>$sum = 154$</li>
</ul>
<blockquote>
<p>If the average of 9 of the numbers in the list is 9,</p>
</blockquote>
<p>We can do the same process and work out the sum of these $9$ numbers:</p>
<ul>
<li>$sum\,of\,9\,numbers= 9 * 9$</li>
<li>$sum\,of\,9\,numbers = 81$</li>
</ul>
<p>We can also deduce the following:</p>
<ul>
<li>$sum\,of\,11\,numbers = sum\,of\,9\,numbers + sum\,of\,remaining\,two\,numbers$</li>
<li>$154 = 81 + sum\,of\,remaining\,two\,numbers$</li>
<li>$73 = sum\,of\,remaining\,two\,numbers$</li>
</ul>
<blockquote>
<p>what is the average of the other 2 numbers?</p>
</blockquote>
<p>Now, we can use the relationship between sum and mean one last time to figure out the average of these two numbers:</p>
<ul>
<li>$mean\,of\,remaing\,two\,numbers = \frac{sum\,of\,remaing\,two\,numbers}{\#\,values}$</li>
<li>$mean\,of\,remaing\,two\,numbers = \frac{73}{2}$</li>
<li>$mean\,of\,remaing\,two\,numbers = 36.5$</li>
</ul>
<p>So, the answer is <span style="color:#27ae60;">36.5</span>.</p>