Problem Solving

If S={0,4,5,2,11,8}, how much greater than the median of the numbers in S is the mean of the numbers in S?

A. 0.5
B. 1.0
C. 1.5
D. 2.0
E. 2.5

Hi there!

Mean is the same as "arithmetic mean" (and you should count the value 0 as you count any other value).

Whenever you find the term "Median", replace it with the term "central" to avoid confusion... when you have an even number of elements in your list (it´s the case), please remember that the median is, by definition, the arithmetic mean of the two "central" values, AFTER you list has been ORDERED (increasingly or decreasingly, it does not matter).

So... from the fact that (1st position+last position)/2 = (1+ 6)/2 = 3.5 that means you have to take the arithmetic mean of the 3th and the 4th term (ordered list, do not forget), so the median is...

You finish it!

Solution: [spoiler]Median= 4.5 = (4+5)/2 and Mean = 30/6 = 5, therefore the answer is 5 - 4.5 = 0.5 , therefore (A)[/spoiler]

Regards,
Fabio.

mean of the given S = (0+2+4+5+8+11)/6 = 5
to obtain the median arrange the S in ascending order S = {0,2,4,5,8,11}
now median is (4+5)/2 = 4.5
hence the difference between mean and median = 5 - 4.5 = 0.5