Question 783669
92, 98, 15, 92, 87, 92

The median is the middle value, so I'll have to rewrite the list in order:

 15,  87, 92, 92 , 92, 98

There are six numbers in the list, so the middle one will be the {{{(6 + 1)/ 2 = 7 / 2 = 3.5th}}} number:

which is {{{92}}} 

The mean is the usual average:

{{{(15+87+92+92 +92+98)/6=79.33}}}

teacher said that his grade would be based on the mean, and we know that
{{{medians}}} are less sensitive to {{{extreme}}}{{{ scores}}} and are probably a {{{better}}}{{{ indicator}}} generally of {{{where}}} the {{{middle}}} of the class is achieving, especially for {{{smaller}}}{{{ sample}}} {{{sizes}}} like here 
{{{means}}} are the {{{arithmetic}}}{{{ average}}} and are often used with {{{larger}}}{{{ sample}}} {{{sizes}}}; 

so, Sam argued that his grade should be based on the median score of his grades and he is {{{right}}} because   {{{ sample}}} {{{size}}} is {{{smal}}} and {{{92}}} is a {{{better}}}{{{ indicator}}}  of his grade