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Set S: {5, 10, 15} If the number 15 were removed from set S
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28 Jul 2018, 16:21
28 Jul 2018, 16:21
Expert Reply
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Question Stats:
86% (00:18) correct
14% (00:14) wrong based on 50 sessions
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Set S: {5, 10, 15}
If the number 15 were removed from set S and replaced with the number 1,000, which of the following values would change?
Indicate all such values.
A. The mean of the set
B. The median of the set
C. The standard deviation of the set
If the number 15 were removed from set S and replaced with the number 1,000, which of the following values would change?
Indicate all such values.
A. The mean of the set
B. The median of the set
C. The standard deviation of the set
Re: Set S: {5, 10, 15} If the number 15 were removed from set S
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11 Aug 2018, 14:10
11 Aug 2018, 14:10
1
The median isn't affected by outliers. It would still be 10, as 10 is the middle value. Mean and standard deviation are. So the answer is A and C.
Re: Set S: {5, 10, 15} If the number 15 were removed from set S
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12 Aug 2018, 16:14
12 Aug 2018, 16:14
Expert Reply
Explanation
The word mean is a synonym for the average. Because an average is calculated by taking the sum of the terms in the set and dividing by the number of numbers in the set, changing any one number in a set (without adjusting the others) will change the sum and, therefore, the average.
The median is the middle number in a set, so making the biggest number even bigger won’t change that (the middle number is still 10). Standard deviation is a measure of how spread out the numbers in a set are—the more spread out the numbers, the larger the standard deviation—so making the biggest number really far away from the others would greatly increase the standard deviation.
The word mean is a synonym for the average. Because an average is calculated by taking the sum of the terms in the set and dividing by the number of numbers in the set, changing any one number in a set (without adjusting the others) will change the sum and, therefore, the average.
The median is the middle number in a set, so making the biggest number even bigger won’t change that (the middle number is still 10). Standard deviation is a measure of how spread out the numbers in a set are—the more spread out the numbers, the larger the standard deviation—so making the biggest number really far away from the others would greatly increase the standard deviation.
