In the 1994 Baseball Strike, the owners stated that the average player's salary was $1.2 million (they used the mean).
This is true, but the median salary was $500,000 -- half the players earned less than that, half more. So, the Players
union stated that the average salary was $500,000.
Now look at the following example of 5 players' salaries:
| Player 1:
|
$5,000,000
|
| Player 2:
|
$4,500,000
|
| Player 3:
|
$900,000
|
| Player 4:
|
$800,000
|
| Player 5:
|
$800,000
|
Compute the mean, median, and mode of this set of numbers: ______________________
ANSWER:
The mean is $2,400,00
The median is $900,000
The mode is $800,000
Any one of these numbers could be used as the "average" salary.
Note that the mean is greater than the median which in turn is greater than the mode.
Is it possible to find a set of numbers whose median is bigger than its mode, which in turn is bigger than its mean?
ANSWER:
No.
If the median is greater than the mode,
Then two numbers less than the median must be the same.
This forces the mean to be bigger than the mode.