Official Guide Explanation:
Problem Solving #148

Background

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Solution and Metadata

Question: 148
Page: 81
Difficulty: 5 (Moderate)
Category 1: Word Problems > Data Interpretation >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Arithmetic > Descriptive Statistics > other

Explanation: The median and mean of a set are equal when the set is symmetrical: that is, for every number that is greater than the median, there is a number less than the median that is equally distant from the median. For instance, in the distribution of X, the median is 40. There are 3 occurences of 30 and 3 occurences of 50; because those values are equidistant from the median in opposite directions, they can be said to "cancel each other out." Since all such values in the distribution of X do that, X's mean is equal to its median.

The same can be true of Z, which is symmetrical. (Note that such symmetry is visual, not just arithmetic.) Y, however, is not symmetrical--there are 5 values of 30 against just 2 values of 50, and 3 values of 60 against only one value of 20. Therefore, since X and Z have equal means and medians, the correct choice is (E).

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