Question 1157998
{{{matrix(2,7,
Score,red(0),red(1),red(2),red(3),red(4),red(5),
Frequency,green(0),green(4),green(1),green(5),green(1),green(3))}}}
 
I see that{{{green(0)}}} students got a score of {{{red(0)}}} ,
{{{green(4)}}} students got a score of {{{red(1)}}} ,
{{{green(1)}}} student got a score of {{{red(2)}}} ,
{{{green(5)}}} students got a score of {{{red(3)}}} ,
{{{green(1)}}} student got a score of {{{red(4)}}} ,
and {{{green(3)}}} students got a score of {{{red(5)}}} .
That means the number of students was
{{{green(4)+green(1)+green(5)+green(1)+green(3)=14}}}
The mean is the average of all those {{{14 scores}}} .
To calculate it I have to add those 14 scores.
I could add
{{{red(1)+red(1)+red(1)+red(1)+red(2)+red(3)+red(3)+red(3)+red(3)+red(3)+"..."}}} .
However, instead of add a score several times, I could just multiply times its frequency, and add the products:
{{{(red(1)*green(4))+(red(2)*green(1))+(red(3)*green(5))+(red(4)*green(1))+(red(5)*green(3))}}} 
Oh! And because centuries ago people doing math all over the world decided to agree that multiplications have priority over addition, I can skip all those parentheses, and write
{{{Sum}}}{{{of}}}{{{all}}}{{{scores}}}{{{"="}}}{{{red(1)*green(4)+red(2)*green(1)+red(3)*green(5)+red(4)*green(1)+red(5)*green(3)=4+2+15+4+15=40}}}
Then, {{{mean=40/14=20/7="2.857142857142857142..."}}}
Round the mean to the nearest hundredth, it says,
so it rounds to 2 and 86/100, because the thousands digit is 7, so we have to round up.
The mean (average) aptitude score is {{{highlight(2.86)}}} 
 
The median of a set of values is the one in the middle when we put the values in order.
And if there is an even number of value, we average the two in the middle.
The 14 scores in order are 
{{{red(1)}}}{{{red(1)}}}{{{red(1)}}}{{{red(1)}}}{{{red(2)}}}{{{red(3),red(3)}}{{{red(3)}}}{{{red(3)}}}{{{red(3)}}}{{{red(4)}}}{{{red(5)}}}{{{red(5)}}}{{{red(5)}}} .

The seventh and eighth values. both {{{red(3)}}} , are the two in the middle, and their average is, of course, {{{red(3)}}} .
 
The median aptitude score is {{{highlight(3)}}} .