Bunuel wrote:
For which of the following lists, the mean is greater than the median?
I. 2/3, 3/4, 4/5, 5/6, 6/7
II. 8/7, 7/6, 6/5, 5/4, 4/3
III. 1/2, 1/3, 1/4, 1/5, 1/6
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
The values in the lists are not equally spaced.
I. 2/3, 3/4, 4/5, 5/6, 6/7
Each next value is obtained by adding 1 to be numerator and the denominator of the previous value. So each value keeps getting closer to 1 and hence keeping greater. The increase is more initially and lesser as we proceed. So 3/4 - 2/3 > 6/7 - 5/6 etc.
Median is the middle value 4/5.
2/3 and 3/4 have more deficit from 4/5 than the excess of 5/6 and 6/7. Hence mean will be less than 4/5.
II. 8/7, 7/6, 6/5, 5/4, 4/3
The values are arranged in increasing order.
Median = 6/5
When we reduce 1 from both numerator and denominator, the values go away from 1. So these values are increasing. They will increase slowly first and then rapidly. So the excess of 5/4 and 4/3 from 6/5 is more than the deficit of 8/7 and 7/6.
Hence mean is greater than 6/5.
III. 1/2, 1/3, 1/4, 1/5, 1/6
The values are arranged in decreasing order.
Median = 1/4.
The excess of 1/2 and 1/3 from 1/4 is more than the deficit of 1/5 and 1/6. Hence mean will be greater than 1/4.
Answer (E)
Also check this post:
https://anaprep.com/sets-statistics-mean-or-median/