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A researcher computed the mean, the median, and the standard

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A researcher computed the mean, the median, and the standard  [#permalink]

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New post 25 Jun 2012, 02:40
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A
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D
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76% (00:37) correct 24% (00:35) wrong based on 1376 sessions

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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

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Question: 9
Page: 21
Difficulty: 650

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Re: A researcher computed the mean, the median, and the standard  [#permalink]

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New post 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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: A researcher computed the mean, the median, and the standard  [#permalink]

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New post 25 Jun 2012, 04:15
Hi,

Difficulty level: 600

When a constant term is added to all values in the series, mean and median change by same value. In this case, both will increase by 5.
The standard deviation doesn't change.

Thus, Answer is (D)

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Re: A researcher computed the mean, the median, and the standard  [#permalink]

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New post 27 Aug 2016, 23:05
If we add or subtract a constant from all the terms in a series, then the mean and median will change by the value of constant. The deviation remains the same.

Hence, D

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Re: A researcher computed the mean, the median, and the standard  [#permalink]

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New post 25 Dec 2016, 22:43
Great Question.
Here
New mean = Old mean +5
New median = Old median +5

New standard deviation = Old standard deviation
Standard deviation just shows the average distance of individual data elements with respect to the mean. Hence it wont change.


Hence D

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Re: A researcher computed the mean, the median, and the standard  [#permalink]

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New post 14 Feb 2018, 11:03
Bunuel wrote:
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


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
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Re: A researcher computed the mean, the median, and the standard &nbs [#permalink] 14 Feb 2018, 11:03
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