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Set A consists of the elements {1,3,5,7}. If Set B consists of the ele
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14 Jun 2023, 05:35
14 Jun 2023, 05:35
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Set A consists of the elements {1,3,5,7}. If Set B consists of the elements {12,14,16,x}, and the standard deviation of Set B is higher than that of Set A, then which of the following is a possible value of x ?
Indicate all such values.
A. 15
B. 16
C. 17
D. 18
E. 19
F. 20
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Indicate all such values.
A. 15
B. 16
C. 17
D. 18
E. 19
F. 20
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) Cracking the GRE Premium
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
Re: Set A consists of the elements {1,3,5,7}. If Set B consists of the ele
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16 Jun 2023, 04:00
16 Jun 2023, 04:00
Expert Reply
OE
Start by finding the mean for Set A—this can be done by
calculating the sum of the set divided by 4, or by observing
that the numbers are evenly spaced, so the sum must be the
average of the two middle numbers. The total variance of the
set (the total distance of the members from the mean) is 8.
Therefore, the possible values of x must create a total
variance for Set B of equal to or greater than 8. Since the
values of Set A are evenly spaced with a difference of 2
between each value, look for the answer choice that creates
the same condition for Set B. The value 18 creates the set {12,
14, 16, 18}, which has a mean of 15 and a total variance from
the mean of 8. This set would thus have the same standard
deviation as that of Set A. Since the question asks for the
values of x that would create a Set B with a higher standard
deviation than that of Set A, x must be greater than 18. The
correct answers are (E) and (F).
Start by finding the mean for Set A—this can be done by
calculating the sum of the set divided by 4, or by observing
that the numbers are evenly spaced, so the sum must be the
average of the two middle numbers. The total variance of the
set (the total distance of the members from the mean) is 8.
Therefore, the possible values of x must create a total
variance for Set B of equal to or greater than 8. Since the
values of Set A are evenly spaced with a difference of 2
between each value, look for the answer choice that creates
the same condition for Set B. The value 18 creates the set {12,
14, 16, 18}, which has a mean of 15 and a total variance from
the mean of 8. This set would thus have the same standard
deviation as that of Set A. Since the question asks for the
values of x that would create a Set B with a higher standard
deviation than that of Set A, x must be greater than 18. The
correct answers are (E) and (F).
gmatclubot
Re: Set A consists of the elements {1,3,5,7}. If Set B consists of the ele [#permalink]
16 Jun 2023, 04:00
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