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21 May 2024, 01:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (01:36) correct
33% (01:12) wrong based on 9 sessions
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The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of the Chinstrap penguins on the island is 13.2 centimeters, and the range of the heights of the Gentoo penguins on the island is 15.4 centimeters.
Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island?
Indicate all such statements.
A. The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
B. The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.
C. The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.
Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island?
Indicate all such statements.
A. The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
B. The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.
C. The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.
06 Jun 2024, 00:58
Kudos
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First, define the range algebraically do determine specifically what value(s) will be sufficient to definitively determine the range of all penguin heights.
So, the range will equal largest penguin - smallest penguin. Already, we know that tallest G - shortest G = 15.4 and that tallest C - shortest C = 13.2.
So, what is needed to determine the total range is the overlap of the two ranges or Tallest G - Shortest C or Tallest C - Shortest G.
Evaluate the choices to determine if any will provide the overlap of the ranges.
A The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
Plug in the information algebraically to find that Tallest G = Tallest C + 5.8.
Therefore, the overall range is determined by Tallest C + 5.8 - Shortest C = 13.2 --> So, the overall range of Tallest G - Shortest C = 7.4, which is a definitive answer, so select Choice A.
B The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.
Median provides no information about the shortest or tallest, so eliminate Choice B.
C The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.
Average provides no information about the shortest or tallest, so eliminate Choice C, leaving only Choice A selected.
So, the range will equal largest penguin - smallest penguin. Already, we know that tallest G - shortest G = 15.4 and that tallest C - shortest C = 13.2.
So, what is needed to determine the total range is the overlap of the two ranges or Tallest G - Shortest C or Tallest C - Shortest G.
Evaluate the choices to determine if any will provide the overlap of the ranges.
A The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
Plug in the information algebraically to find that Tallest G = Tallest C + 5.8.
Therefore, the overall range is determined by Tallest C + 5.8 - Shortest C = 13.2 --> So, the overall range of Tallest G - Shortest C = 7.4, which is a definitive answer, so select Choice A.
B The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.
Median provides no information about the shortest or tallest, so eliminate Choice B.
C The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.
Average provides no information about the shortest or tallest, so eliminate Choice C, leaving only Choice A selected.
26 Jun 2024, 12:29
Kudos
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Official Explanation
Choice A tells you that the tallest Gentoo penguin is 5.8 centimeters taller than the tallest Chinstrap penguin. You can combine this information with the given information about the Gentoo and Chinstrap height ranges to place four penguins—the shortest Gentoo, the shortest Chinstrap, the tallest Gentoo, and the tallest Chinstrap—in relative order according to height, as shown in the figure below.
You can see from the figure that the tallest penguin must be a Gentoo and the shortest penguin must be a Chinstrap. You can also see the difference in height between those two penguins, which is the range of the heights of all the penguins. Therefore, Choice A provides sufficient additional information to determine the range.
Choice B provides information about one of the centers of the data—the median; it does not say anything about how spread out the data are around that center. You are given that the median height of the Gentoos is 1.1 centimeters greater than that of the Chinstraps. First note that it is possible for two different sets of data to have the same median but have very different ranges. Choice B gives the difference between the medians of the Gentoo heights and the Chinstrap heights, without giving the actual medians. However, even if you knew the medians, the fact that the ranges can vary widely indicates that the range of the heights of all the penguins can also vary widely.
It is possible to construct examples of heights of penguins that satisfy all of the information in the question and in Choice B but have different ranges for the heights of all the penguins. Here are two such examples, each of which has only three Chinstraps and three Gentoos. Although the examples are small, they illustrate the fact that the range of the heights of all the penguins can vary. In both examples, the range of Chinstrap heights is 13.2 centimeters, the range of Gentoo heights is 15.4 centimeters, and the difference between the median heights is 1.1 centimeters.
Therefore, Choice B does not provide sufficient additional information to determine the range of the heights of all the penguins.
Choice C provides information about another center of the data—the average. You are given that the average height of the Gentoos is 4.6 centimeters greater than that of the Chinstraps. However, like Choice B, the statement gives no information about how spread out the data are around that center. Again, it is possible for two different sets of data to have the same average but have very different ranges. Examples similar to the two examples above can be constructed that satisfy all of the information in the question and in Choice C but have different ranges for the heights of all the penguins. Therefore, Choice C does not provide sufficient additional information to determine the range of the heights of all the penguins.
The correct answer consists of Choice A.
Choice A tells you that the tallest Gentoo penguin is 5.8 centimeters taller than the tallest Chinstrap penguin. You can combine this information with the given information about the Gentoo and Chinstrap height ranges to place four penguins—the shortest Gentoo, the shortest Chinstrap, the tallest Gentoo, and the tallest Chinstrap—in relative order according to height, as shown in the figure below.
You can see from the figure that the tallest penguin must be a Gentoo and the shortest penguin must be a Chinstrap. You can also see the difference in height between those two penguins, which is the range of the heights of all the penguins. Therefore, Choice A provides sufficient additional information to determine the range.
Choice B provides information about one of the centers of the data—the median; it does not say anything about how spread out the data are around that center. You are given that the median height of the Gentoos is 1.1 centimeters greater than that of the Chinstraps. First note that it is possible for two different sets of data to have the same median but have very different ranges. Choice B gives the difference between the medians of the Gentoo heights and the Chinstrap heights, without giving the actual medians. However, even if you knew the medians, the fact that the ranges can vary widely indicates that the range of the heights of all the penguins can also vary widely.
It is possible to construct examples of heights of penguins that satisfy all of the information in the question and in Choice B but have different ranges for the heights of all the penguins. Here are two such examples, each of which has only three Chinstraps and three Gentoos. Although the examples are small, they illustrate the fact that the range of the heights of all the penguins can vary. In both examples, the range of Chinstrap heights is 13.2 centimeters, the range of Gentoo heights is 15.4 centimeters, and the difference between the median heights is 1.1 centimeters.
Therefore, Choice B does not provide sufficient additional information to determine the range of the heights of all the penguins.
Choice C provides information about another center of the data—the average. You are given that the average height of the Gentoos is 4.6 centimeters greater than that of the Chinstraps. However, like Choice B, the statement gives no information about how spread out the data are around that center. Again, it is possible for two different sets of data to have the same average but have very different ranges. Examples similar to the two examples above can be constructed that satisfy all of the information in the question and in Choice C but have different ranges for the heights of all the penguins. Therefore, Choice C does not provide sufficient additional information to determine the range of the heights of all the penguins.
The correct answer consists of Choice A.
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