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06 Jun 2022, 02:15
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Which of the following sets has the greatest standard deviation?
A. {2, 2, 5, 8, 8}
B. {3, 4, 5, 6, 7}
C. {1, 3, 5, 7, 9}
D. {3, 3, 5, 7, 7}
E. {0, 3, 5, 7, 10}
A. {2, 2, 5, 8, 8}
B. {3, 4, 5, 6, 7}
C. {1, 3, 5, 7, 9}
D. {3, 3, 5, 7, 7}
E. {0, 3, 5, 7, 10}
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06 Jun 2022, 06:52
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Which of the following sets has the greatest standard deviation?
In all the sets 5 is the avg.
consider that each set is evenly distributed with respect to its avg. We can leverage this fact and consider only the square difference from the avg of first 2 term of each set
A. {2, 2, 5, 8, 8} -> \(3^2+3^2=18\)
B. {3, 4, 5, 6, 7} -> \(2^2+1^2=5\)
C. {1, 3, 5, 7, 9} -> \(4^2+2^2=20\)
D. {3, 3, 5, 7, 7} -> \(2^2+2^2=8\)
E. {0, 3, 5, 7, 10} -> \(5^2+2^2=29\)
feedback appreciated
In all the sets 5 is the avg.
consider that each set is evenly distributed with respect to its avg. We can leverage this fact and consider only the square difference from the avg of first 2 term of each set
A. {2, 2, 5, 8, 8} -> \(3^2+3^2=18\)
B. {3, 4, 5, 6, 7} -> \(2^2+1^2=5\)
C. {1, 3, 5, 7, 9} -> \(4^2+2^2=20\)
D. {3, 3, 5, 7, 7} -> \(2^2+2^2=8\)
E. {0, 3, 5, 7, 10} -> \(5^2+2^2=29\)
feedback appreciated
06 Jun 2022, 07:44
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Bunuel
Which of the following sets has the greatest standard deviation?
A. {2, 2, 5, 8, 8}
B. {3, 4, 5, 6, 7}
C. {1, 3, 5, 7, 9}
D. {3, 3, 5, 7, 7}
E. {0, 3, 5, 7, 10}
A. {2, 2, 5, 8, 8}
B. {3, 4, 5, 6, 7}
C. {1, 3, 5, 7, 9}
D. {3, 3, 5, 7, 7}
E. {0, 3, 5, 7, 10}
GMAC never asks us to actually calculate standard deviation. All they test us on is the concept that standard deviation is a measure of how wide a distribution is, and the wider the distribution, the larger the standard deviation.
All of the sets have a median 5. Let's just compare answer choices.
Comparing A and B: 3 and 4 are closer to 5 than 2 and 2 are. 6 and 7 are also closer to 5 than 8 and 8 are. So A has a greater standard deviation. B is wrong.
Glancing at C, D, and E, their middle three terms are all 3, 5, 7, so the only impact on their standard deviations will come from the first and last terms. E is farthest from the median for first and last terms. C and D are wrong.
Comparing A and E: The second and fourth terms of A are farther from the median than are the second and fourth terms of E, but only by one. The first and fifth terms of E are farther from the median than are the first and fifth terms of A by two. On the balance, E is more widely distributed.
Answer choice E.
