PSAT Math Multiple-Choice Question 544: Answer and Explanation

Question: 544

The following data represents the shoulder heights in meters (m) of 7 elephants that live in a local zoo.

Elephant	Shoulder Height (m)
A	2.04
B	1.83
C	2.13
D	3.14
E	2.45
F	2.68
G	1.90
H	?

An additional elephant is added to the zoo, and its shoulder height is measured. Its shoulder height increases the median value of the group of elephants but decreases the mean value of the group. What is a possible measurement for the shoulder height of the 8th elephant?

• A. 1.98 m
• B. 2.13 m
• C. 2.24 m
• D. 2.31 m

Correct Answer: C

Explanation:

C

The question asks for a new data point based on how it changes the mean and median of a set of data. The median is easier to determine, so start by finding the median of the existing data. The median of a list of numbers is the middle number when all values are arranged in order. The shoulder heights are not listed in order, so start by listing the shoulder heights from shortest to tallest. Elephant B has the shortest shoulder height of 1.83 meters. Elephant G has the 2nd shortest shoulder height of 1.90 meters, and Elephant A has the 3rd shortest shoulder height of 2.04 meters. Elephant C, Elephant E, Elephant F, and Elephant D have shoulder heights of 2.13, 2.45, 2.68, and 3.14 meters, respectively. Therefore, the median shoulder height of the original 7 elephants is 2.13 meters. The question states that Elephant H's shoulder height increases the median value of the group of elephants. Eliminate (A) which is smaller than 2.13 meters and would decrease the median value. Eliminate (B) which matches the median and therefore would not increase it. The question also refers to a change in the mean or average value, so calculate the average shoulder height. Use the formula T = AN, where T is the total, A is the average, and N is the number of things. The total is 1.83 + 1.90 + 2.04 + 2.13 + 2.45 + 2.68 + 3.14 = 16.17, and the number of things is 7. The equation becomes 16.17 = A(7). Divide both sides by 7 to get A = 2.31. The question states that Elephant H's shoulder height decreases the mean value of the group. Eliminate (D), as this value is equal to the mean and would keep the mean the same. The correct answer is (C).