Question

What are the mean, median, and mode salaries of a baseball team where the 24 players earn the following annual salaries: 2 players at $14.6 million; 4 at $7.45 million; 4 at 3.93 million; 5 at $450,000; 2 at $390,000 and 7 at $200,000?

Answer 1

Mean, `bar x=1/nsum_(I=1)^nx_i=$3297917`
Median = $450000.
Mode = $200000

Explanation:

Start by arranging all the data points in increasing order to obtain :

200000
200000
200000
200000
200000
200000
200000
390000
390000
450000
450000
450000
450000
450000
3930000
3930000
3930000
3930000
7450000
7450000
7450000
7450000
14600000
14600000

Define `X={x_i}` to be the set of these data points in this order.

Now by definition, the mean or average of these values is given by
`bar x=1/nsum_(I=1)^nx_i=3297917`

The median is defined to be the centre data point or, in this case since the number of data points is an even number, the mean of the 2 centre points, ie `(450000+450000)/2=450000`

The mode is defined to be the data point which occurs most often, so in this case it is 200000 which occurs 7 times in the sample space.