Standard Deviation- Manhattan

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venmic: Master | Next Rank: 500 Posts; Posts: 222; Joined: Mon Oct 13, 2008 4:04 pmFollowed by: 2 members; Thanked: 3 times

by venmic » Sun Oct 09, 2011 8:43 pm

Let Set T = {2, 4, 5, 7}. Which of the following values, if added to Set T, would most increase the standard deviation of Set T?

1

3

6

8

14

14

Can anyone give me the step by step explanation of how to solve this problem

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sun Oct 09, 2011 9:09 pm

My solution: standard deviation (sd) means how far the numbers are from the mean...
the present numbers are 2,4,5,7
if we add 3 or 6, they lie in the range only and similarly 1,8 re just next to 2 and 7 respectively which are already in the set. 14 is too far from 7, and thus will increase sd the most

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sun Oct 09, 2011 9:16 pm

Looking at the answer choices we can find that 14 is way off from the given set of numbers while the other 4 numbers are pretty close to each other. We could say 14 would be the answer from the choices, if you are looking to solve it using math, we need to consider each case and do it separately.

First find SD of {2, 4, 5, 7}

SD = Sqrt(Mean of squares - Square of Mean)

Mean = 18/4 = 4.5

Mean of squares = (4+16+25+49)/4 = 23.5

SD = Sqrt(23.5 - 20.25) = 1.8

Now for eg, add number 6 to the above set of Nos;

Mean = 4.8

Mean of squares = (4+16+25+36+49)/5 = 26

SD = Sqrt(26 - 23.08) = 1.7 (which is less than 1.8)

Similarly try for a bigger No. Only adding 14 would be above 1.8

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Oct 09, 2011 9:35 pm

venmic wrote:Let Set T = {2, 4, 5, 7}. Which of the following values, if added to Set T, would most increase the standard deviation of Set T?

Standard deviation is nothing but the average distance of the samples from the mean. A low standard deviation indicates that the samples are very close to the mean, whereas high standard deviation indicates that the samples are spread out over a large range of values.

Hence, out of the options 14 will increase the range of the of the set T. Hence adding 14 to the set T will increase the standard deviation of Set T.

The correct answer is E.

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venmic: Master | Next Rank: 500 Posts; Posts: 222; Joined: Mon Oct 13, 2008 4:04 pmFollowed by: 2 members; Thanked: 3 times

by venmic » Sun Oct 16, 2011 9:30 pm

Since

1 2, 4, 5, 7 range = 6
3 2, 4, 5, 7 range = 5
6 2, 4, 5, 7 range =5
8 2, 4, 5, 7 range = 6
14 2, 4, 5, 7 range = 12

So since the range when 14 is added is the greatest 14 is the answer ? can we always go by that logic

Anurag@Gurome wrote:
venmic wrote:Let Set T = {2, 4, 5, 7}. Which of the following values, if added to Set T, would most increase the standard deviation of Set T?
Standard deviation is nothing but the average distance of the samples from the mean. A low standard deviation indicates that the samples are very close to the mean, whereas high standard deviation indicates that the samples are spread out over a large range of values.

Hence, out of the options 14 will increase the range of the of the set T. Hence adding 14 to the set T will increase the standard deviation of Set T.

The correct answer is E.

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon Oct 17, 2011 1:26 am

IMO:E

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masoom j negi: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Thu Dec 20, 2018 2:09 am

by masoom j negi » Fri Dec 21, 2018 9:03 pm

Any number that will be farthest from the mean of the set will change the standard deviation the most.
Here mean of the set is 18/4 = 4.5.
Since we have to increase the standard deviation we can't take any value that is less than the mean. So , 1 and 3 are not acceptable.
From 6, 8 and 14, clearly 14 is farthest from the mean. So, it will increase the standard deviation the most.
Hence, 14 is the answer.

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