Can anyone me out with this statistics question i’m having difficulty understanding the context of each answer choice
which of the following statements is supported by the bar chart?
a) for students who chose art, the number of grade 8 students was at least 100% greater than the number of grade 7 students.
b) for students who chose social studies, the number of grade 8 students was at least 100% greater than the number of grade 7 students.
c) for students who chose science, the number of grade 8 students was at least 50% less than the number of grade 7 students.
d) for students who chose math, the number of grade 8 students was at least 50% less than the number of grade 7 students.
e) for students who chose language arts, the number of grade 8 students was at least 100% greater than the number of grade 7 students.

  A)  For students who chose art, the number of grade 8 students was at least 100% greater than the number of grade 7 students

Explanation:

Each of the answer choices is making a statement about one of the pairs of bars on the bar chart. It is asking you to relate the top bar (number of grade 8 students) to the bottom bar (number of grade 7 students). The pairs of bars being looked at are in the same order as the answer choices, top to bottom.

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A) "Students who chose art" refers to the top set of bars. The statement whose truth you are to assess is, effectively, "the top bar is more than twice the length of the bottom bar." (It is, so this is the correct answer choice.)

Since the length of the bar is representative of the number of students, when you say "the number of grade 8 students is at least 100% greater than the number of grade 7 students", you mean "the top bar is at least 100% longer than the bottom bar." The top bar will be exactly 100% longer if it is as long again as the bottom bar already is (100% +100% more), meaning the top bar will be exactly double the length of the bottom bar.

We judge the top bar to be more than twice the length of the bottom bar, so the description is true.

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B) Choice B refers to the second set of bars from the top, those students who chose Social Studies. The same relationship is being described: the top bar is more than twice the length of the bottom bar. Since it is not that long, this description is false.

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C) Here, the statement in the answer choice is that the length of the top bar is more than 50% less than the length of the bottom bar. If it were exactly 50% less, it would be half the length of the bottom bar. The statement is that it is less than half the length, apparently false.

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D) Math students are represented by the set of bars second from the bottom. Again the "at least 50% less" relation means you're looking to see if the top bar is less than half the length of the bottom bar. Once again, it is longer than that, so the statement about it is apparently false.

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E) For the bottom set of bars, we're back to the "100% greater" relationship. The top bar is not more than double the bottom bar, so this statement is apparently false.

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