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A certain list of 300 test scores has an arithmetic mean

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by VJesus12 » Mon Apr 08, 2019 5:46 am

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A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?

(A) 75 and 80
(B) 80 and 85
(C) 70 and 75
(D) 75 and 75
(E) 70 and 80

[spoiler]OA=D[/spoiler]

Source: Veritas Prep
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by Sid13791 » Mon Apr 08, 2019 11:56 am
IT's pretty simple . closer the values to the average , lesser will be the deviation .
hence the answer is D
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by Sid13791 » Mon Apr 08, 2019 1:26 pm
VJesus12 wrote:A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?

(A) 75 and 80
(B) 80 and 85
(C) 70 and 75
(D) 75 and 75
(E) 70 and 80

[spoiler]OA=D[/spoiler]

Source: Veritas Prep
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by Scott@TargetTestPrep » Wed Apr 10, 2019 4:34 pm
VJesus12 wrote:A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d?

(A) 75 and 80
(B) 80 and 85
(C) 70 and 75
(D) 75 and 75
(E) 70 and 80

[spoiler]OA=D[/spoiler]

Source: Veritas Prep
Since the mean is 75, we see that when we add 75 and 75 to the list the standard deviation must decrease. Note: Depending on the value of d, the other choices might or might not decrease the standard deviation.

Answer: D

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