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25 Jun 2012, 02:40
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D
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Difficulty:
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Question Stats:
79% (00:46) correct
21%
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A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the median
(E) The mean and the standard deviation
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the median
(E) The mean and the standard deviation
25 Jun 2012, 02:41
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SOLUTION
A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the median
(E) The mean and the standard deviation
If we add or subtract a constant to each term in a set the standard deviation will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the median
(E) The mean and the standard deviation
If we add or subtract a constant to each term in a set the standard deviation will not change..
If we add (or subtract) a constant to each term in a set the mean and the median will increase (decrease) by the value of that constant.
Answer: D.
14 Feb 2018, 11:03
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Bunuel
When a constant number is added to all the elements of a data set, the mean and median increase by the same amount as the added constant, but the standard deviation does not change. Thus, the statistics that change are the mean and median.
If we did not know this fact, we could still find the answer by coming up with an example easy enough to calculate all three quantities. For instance, let’s take a set where all the scores are equal, such as three scores of 10. In the original set, both mean and median are equal to 10; but the standard deviation is 0 (since standard deviation is a measure of how far away the elements are from the mean). When we add 5 to each element, we get three scores of 15; thus, the mean and median both increase to 15, but the standard deviation is still 0.
Answer: D
