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07 Jul 2021, 06:45
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The graph on the left represents the number of family members per family in Town X, while the graph on the right represents the number of family members per family in Town Y. The median family size for Town X is equal to the median family size for Town Y. The horizontal and vertical dimensions of the boxes above are
identical and correspond to the same measurements. Which of the following must be true?
I. The range of family sizes measured as the number of family members is larger in Town X than in Town Y.
II. Families in Town Y are more likely to have sizes within 1 family member of the mean than are families in Town X.
III. The data for Town X has a larger standard deviation than the data for Town Y.
A. I only.
B. II only.
C. III only.
D. II and III only.
E. I, II and III.
Attachment:
2021-06-18_22-30-29.png [ 31.95 KiB | Viewed 7274 times ]
The graph on the left represents the number of family members per family in Town X, while the graph on the right represents the number of family members per family in Town Y. The median family size for Town X is equal to the median family size for Town Y. The horizontal and vertical dimensions of the boxes above are
identical and correspond to the same measurements. Which of the following must be true?
I. The range of family sizes measured as the number of family members is larger in Town X than in Town Y.
II. Families in Town Y are more likely to have sizes within 1 family member of the mean than are families in Town X.
III. The data for Town X has a larger standard deviation than the data for Town Y.
A. I only.
B. II only.
C. III only.
D. II and III only.
E. I, II and III.
As can be seen from the graph we do not know higher and lower values of data points in both the graphs. Therefore range can be equal/more/less. We don't know
II. Since the shape of variance of the graph of town Y is less ( due to less spread), within 1 family member talks about "closer to the mean". True.
III. Spread says it all. Town Y has a less variance and therefore less std dev. True.
Answer D
Attachment:
2021-06-18_22-30-29.png
28 Aug 2021, 07:43
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What we can take from the graph: There are more families in town X since the graph covers more area.
I: The range is unknown as both graphs cover both left and right endpoints of the entire x-axis.
II. This is true as the data for Y is centered around the median.
III. Standard deviation tells us how widespread the points are. Y has a lower standard deviation because most of the points are around the median/average. Thus X has a higher standard deviation.
Ans: D
