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  3. The range of the heights of the female students in a certain class is 13.2 inche

The range of the heights of the female students in a certain class is 13.2 inche

游客2025-02-24  23
问题 The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches.
Which of the following statements individually provide(s)sufficient additional information to determine the range of the heights of all the students in the class?
Indicate all such statements.
选项 A、The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
B、The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
C、The average(arithmetic mean)height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.
答案 A
解析 Choice A tells you that the tallest male student is 5.8 inches taller than the tallest female student. You can combine this information with the given information about the male and female height ranges to place four students—the shortest male, the shortest female, the tallest male, and the tallest female—in relative order according to height, as shown in the figure below.

    You can see from the figure that the tallest student must be a male and the shortest student must be a female. You can also see the difference in height between those two students, which is the range of the heights of the entire class. 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 males is 1.1 inches greater than that of the females. 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 male heights and the female 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 the entire class can also vary widely.
    It is possible to construct examples of heights of students that satisfy all of the information in the question and in Choice B but have different ranges for the heights of the entire class. Here are two such examples, each of which has only three females and three males. Although the examples are small, they illustrate the fact that the range of the heights of the entire class can vary. In both examples, the range of female heights is 13.2, the range of male heights is 15.4, and the difference between the median heights is 1.1 inches.
Example 1
Female heights: 50.0 56.6 63.2 which have a median of 56.6
Male heights: 50.0 57.7 65.4 which have a median of 57.7
Range of heights of entire class: 15.4
Example 2
Female heights: 50.0 56.6 63.2 which have a median of 56.6
Male heights: 51.0 57.7 66.4 which have a median of 57.7
Range of heights of entire class: 16.4
Therefore, Choice B does not provide sufficient additional information to determine the range of the heights of the entire class.
    Choice C provides information about another center of the data—the average. You are given that the average height of the males is 4.6 inches greater than that of the females. 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 the entire class. Therefore, Choice C does not provide sufficient additional information to determine the range of the heights of the entire class.
    The correct answer consists of Choice A.
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