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A certain list of 300 test scores has an arithmetic mean of 75 and a s

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A certain list of 300 test scores has an arithmetic mean of 75 and a s  [#permalink]

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New post 19 Aug 2015, 03:23
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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

Kudos for a correct solution.

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Re: A certain list of 300 test scores has an arithmetic mean of 75 and a s  [#permalink]

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New post 19 Aug 2015, 03:28
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Bunuel 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

Kudos for a correct solution.


If we need to reduce the SD for a set, then we need add the numbers which are closer to the Mean. Since adding a number closer to the mean will shrink the set.

Since the numbers 75 & 75 are equal to the mean, this will reduce the SD.

So the answer is D.
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Re: A certain list of 300 test scores has an arithmetic mean of 75 and a s  [#permalink]

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New post 19 Aug 2015, 04:00
Bunuel 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


Ans: D

Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.
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Re: A certain list of 300 test scores has an arithmetic mean of 75 and a s  [#permalink]

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New post 23 Aug 2015, 12:45
Bunuel 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

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

As discussed HERE, the standard deviation of a set measures the deviation from the mean. A low standard deviation indicates that the data points are very close to the mean whereas a high standard deviation indicates that the data points are spread far apart from the mean.

When we add numbers that are far from the mean, we are stretching the set and hence, increasing the SD. When we add numbers which are close to the mean, we are shrinking the set and hence, decreasing the SD.

Therefore, adding two numbers which are closest to the mean will shrink the set the most, thus decreasing SD by the greatest amount.

Numbers closest to the mean are 75 and 75 (they are equal to the mean) and thus adding them will decrease SD the most.

Answer: D.
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Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A certain list of 300 test scores has an arithmetic mean of 75 and a s  [#permalink]

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New post 24 Dec 2016, 00:47
Great Question.
Here is what i did in this one =>

Using the Basic definition of standard deviation => It is just a statistical tool that is used to measure the average dispersion/variation/deviation/distance of individual data elements with respect to the arithmetic mean => To reduce this we should add data values as close to the mean as possible.

Hence for a compulsory decrease in standard deviation => We should add 75,75(As mean =75)

Hence D

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Re: A certain list of 300 test scores has an arithmetic mean of 75 and a s  [#permalink]

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New post 19 Dec 2017, 21:42
To minimize standard deviation, dispersion of the data-points or values should be minimum aroung the mean i.e. selected values should be near the mean.
Best points would be values equal to mean.
Re: A certain list of 300 test scores has an arithmetic mean of 75 and a s &nbs [#permalink] 19 Dec 2017, 21:42
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