Bunuel wrote:
If the variables, X, Y, and Z take on only the values 10, 20, 30, 40, 50, 60, or 70 with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?
(A) X only
(B) Y only
(C) Z only
(D) X and Y
(E) X and Z
Responding to a pm:
Go back to the basics. What is mean? It's the average, the single value that can represent all the values. How do you find it? You multiply each value by its frequency, add them all up and divide by the sum of the frequencies.
What is the mean of: 10, 20, 30 - we know it is 20
What is the mean of: 10, 10, 20, 30, 30 - again 20. Why? Because if there is one value '10' which is 10 less than 20, then there is also a value '30' which is 10 more than 20. So effectively, both 10 and 30 give us two 20s.
Similarly, here X is: 10, 20, 20, 30, 30, 30, 40, 40, 40, 40, 50, 50, 50, 60, 60, 70
40 is the mean because we have three 30s and three 50s to balance out. We have two 20s and two 60s to balance out and we have a 10 and a 70 to balance out again.
What is median? Median is the middle value when you arrange the numbers in increasing/decreasing order. We can see that 40 will be the middle value too since there are equal number of total elements on both sides of 40. We have 6 elements smaller than 40 and 6 elements greater than 40. Hence median = 40.
Hence, mean = median for X.
We can reason out the same thing for Z too in exactly the same way.
The only possible answer is (E). I don't have to worry about Y.