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Set X consists of 100 numbers. The average (arithmetic mean) of set
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22 Jun 2026, 05:00
22 Jun 2026, 05:00
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Question Stats:
66% (00:52) correct
33% (02:02) wrong based on 9 sessions
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Set X consists of 100 numbers. The average (arithmetic mean) of set X is 10 , and the standard deviation is 4.6 . Which of the following two numbers, when added to set X , will decrease the set's standard deviation by the greatest amount?
A. -100 and -100
B. -10 and -10
C. 0 and 0
D. 0 and 20
E. 10 and 10
A. -100 and -100
B. -10 and -10
C. 0 and 0
D. 0 and 20
E. 10 and 10
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Joined: 20 Feb 2017
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Re: Set X consists of 100 numbers. The average (arithmetic mean) of set
[#permalink]
24 Jun 2026, 06:05
24 Jun 2026, 06:05
1
Expert Reply
Explanation
Let the original set have:
n=100
mean=10
standard deviation=4.6
The standard deviation measures spread around the mean. To decrease the standard deviation as much as possible when adding one number, we want to add a value that is as close as possible to the current mean.
The current sum of squared deviations is
\(100(4.6)^2=2116.\)
If a number x is added, the new variance depends on (x−10)^2. The smaller (x−10)^2 is, the more the standard deviation decreases.
Therefore, among the two choices, compute each distance from 10: \(∣x_{1}-10∣ and ∣x_{2} -10∣.\)
The number closer to 10 will produce the greater decrease in standard deviation.
Answer: E
Let the original set have:
n=100
mean=10
standard deviation=4.6
The standard deviation measures spread around the mean. To decrease the standard deviation as much as possible when adding one number, we want to add a value that is as close as possible to the current mean.
The current sum of squared deviations is
\(100(4.6)^2=2116.\)
If a number x is added, the new variance depends on (x−10)^2. The smaller (x−10)^2 is, the more the standard deviation decreases.
Therefore, among the two choices, compute each distance from 10: \(∣x_{1}-10∣ and ∣x_{2} -10∣.\)
The number closer to 10 will produce the greater decrease in standard deviation.
Answer: E
gmatclubot
Re: Set X consists of 100 numbers. The average (arithmetic mean) of set [#permalink]
24 Jun 2026, 06:05
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