The numbers in set A denote the distance of certain positive integers

Question

The numbers in set A denote the distance of certain positive integers from -1 on the number line. The numbers in set B denote the distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets A and B?

A. Standard Deviation (A) = Standard Deviation (B)

B. Standard Deviation (A) = - Standard Deviation (B)

C. Standard Deviation (A) = Standard Deviation (B) + 2

D. Standard Deviation (A) = 2* Standard Deviation (B)

E. None of the above

LeoN88 · Answer

Let the numbers be 1, 2 and 3.

Let's construct the sets:

A= {2,3,4} Mean= 3
B= {0,1,2} Mean= 1

We see for both the sets the elements are equally dispersed. So, A.

Alternatively
SD1= (1+0+1)/3 SD for A

SD2=(1+0+1)/3 SD for B

IanStewart · Answer

If we have a set of positive integers, each integer's distance to -1 is going to be exactly two greater than its distance to 1. So we have two different sets of distances, and each value in one set is 2 greater than a value in the other set. Increasing every value in a set by a adding a constant doesn't change standard deviation at all, so A is the answer.

nick1816 · Answer

Correct Answer but you should do a slight amendment in your solution.

Standard deviation of A= \sqrt{\frac{1^2+0^2+1^2}{3}} 
Standard deviation of A=  \sqrt{2/3}

LeoN88 · Answer

What you've mentioned is the correct formula for SD. GMAT will never ask you to calculate SD so the question'll be either tricky or can be solved based on extrapolation. I got this method on GC that SD of any set of numbers can be calculated like mean of distance from mean. (Actually it's root of mean of squared distance of elements from mean) Since we don't have time to d such long calculations hence the trick shortcut.

PietroCavallo · Answer

I totally agree with your explanation but isn't answer (A) saying -SD(A) = SD(B)? basically stating they have opposite values? I think answer B why stating -SD(A) = -SD(B) should be the correct one, no? Am i missing something?

IanStewart · Answer

Whoever typed up the question made things confusing -- I see your point, and because of the way the answer choices are typed, with a hyphen after each letter A, B, C, D and E, you might think there are negative signs in front of each equation. Whoever typed the question intended for the answers to look like this (clear because a negative sign would make no sense at the beginning of answer E) :

A) Standard Deviation (A) = Standard Deviation (B) 
 B) Standard Deviation (A) = - Standard Deviation (B) 
 etc

though no real GMAT question would write equations in this way regardless.

The numbers in set A denote the distance of certain positive integers

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The numbers in set A denote the distance of certain positive integers

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