whats the best process to find the sd for this?

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

whats the best process to find the sd for this?

by oquiella » Sat Sep 05, 2015 10:15 am

Which of the following lists has the third largest standard deviation?

{1, 2, 3, 4, 5}

{2, 3, 3, 3, 4}

{2, 2, 3, 3, 5}

{1, 2, 3, 4, 6}

{1, 3, 4, 5, 7}

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Source: Beat The GMAT — Problem Solving | Sat Sep 05, 2015 10:15 am

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by [email protected] » Sat Sep 05, 2015 1:53 pm

Hi oquiella,

Standard Deviation is a relatively rare concept on Test Day (you'll likely see it just once), so it's not a big 'point-gainer' or 'point-loser.' The GMAT will never ask you to actually calculate a Standard Deviation either; you will be tested on your general understanding of the concept though.

In real basic terms, SD is about how 'spread out' a group of numbers is: the more spread out the numbers are, the higher the SD. The closer the numbers are together, the smaller the SD.

In this prompt, we can use the answer choices to 'visually compare' how close the numbers are to one another in each set of numbers.

In Answer A, we have numbers that are evenly spaced out. Compare that set with the set in Answer B:

Answer A: {1,2,3,4,5}
Answer B: {2,3,3,3,4}

Notice how Answer B's numbers are 'closer together' (the 1 and the 5 in Answer A are replaced by a 2 and a 4 in Answer B).

Now, compare Answer C with Answer A: which group of numbers is 'closer together'? You should notice that the numbers in Answer C are ALSO 'closer together' than the numbers in Answer A. Now we have two answers that have a SMALLER SD than Answer A.

In that same way, how would you describe the 'spread' in Answers D and E, relative to the spread in Answer A. Can you define how they both have a GREATER spread? What would that mean about their SDs, relative to Answer A?

In the end, just by using the concept behind SD, we've found two answers that have greater SDs and two answers that have smaller SDs (relative to Answer A), thus Answer A is the third largest SD of the group.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sat Sep 05, 2015 1:54 pm

Which of the following data sets has the third largest standard deviation?
A) {1, 2, 3, 4, 5}
B) {2, 3, 3, 3, 4}
C) {2, 2, 2, 4, 5}
D) {0, 2, 3, 4, 6}
E) {-1, 1, 3, 5, 7}

So far, all of the official GMAT questions involving standard deviation (comparing the standard deviations of several lists of numbers) that I've seen can be answered by "eyeballing" the values and comparing how spread apart they are.

So, for example, the values in E are spread apart the most, so E has the greatest SD.
The values in D are spread apart the second most, so D has the second greatest SD.

Now let's look at the values are packed together the most.
The values in B are the most tightly packed, so B has the smallest SD
The values in C are next most tightly packed, so C has the second smallest SD

So, the SDs from least to greatest are: B, C, A, D, E

So A has the third largest standard deviation..

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770