# Whats the difference between class average and class median?

Feb 16, 2017

There are several kinds of averages, but ordinarily it is assumed to be the arithmetic mean. The median, also regarded loosely as an 'average', is calculated in a different way.

#### Explanation:

Let us consider this list of numbers which, for convenience. are listed in numeric order:

$4 , 7 , 8 , 12 , 13 , 16 , 20 , 21$

To get the arithmetic mean, add the numbers together to get the sum. Count the numbers to get the count. Divide the sum by the count to get the arithmetic mean.

$4 + 7 + 8 + 12 + 13 + 16 + 20 + 21 = 101 \to$ the sum.

There are $8$ numbers, so

$\frac{101}{8} = 12.625$

The arithmetic mean is $12.625$.

For the median, take the list of numbers in numeric order and count them i.e. 8. Look for the middle number in the list.

If there is an uneven count of numbers (say we left out $13$ from the list) then $12$ would be the median - the middle number. But, because $8$ is an even number, there are two numbers in the middle - $12$ or $13$ - depending on from which end of the list you start counting.

In this case, divide the sum of the middle numbers

$\frac{12 + 13}{2} = \frac{25}{2} = 12.5$

The median is $12.5$.

Some lists of numbers allow duplicates. In that case there may be more than two middle numbers.

For example, take

$4 , 5 , 6 , 7 , 7 , 7 , 8 , 9$

To get the median, add the middle numbers

$7 + 7 + 7$

and divide by their count, i.e. $3$. The median would be

$\frac{21}{3} = 7$