Are the standard deviations of set A and set B the same? 1) n=6 2) S

Question

Are the standard deviations of set A and set B the same?

1) n = 6
2) Set A = {n, 2, 2, 2} and set B = {n, n, n, 2}

mikemcgarry · Accepted Answer

Dear AustinKL , I'm happy to respond. :-)

This is a great question! You may find this blog article germane: Standard Deviation on the GMAT Statement #1 : n = 6 Obviously, this statement, alone and by itself, is not sufficient . Statement #1 : Set A = {n, 2, 2, 2} and set B = {n, n, n, 2} This statement is the meat of the question! Standard deviation is a way to measure the spread of a set. It only depends on the spacing of the numbers. Here's what I mean. Consider Set #1 = {1, 4, 9, 16, 25} That's the first five squares. The "spacings" in that set could be written as _3_5_7_9_. Any other set with that same pattern of spacing, or the mirror image, would have the same SD. Such other sets would include: Set #2 = {21, 24, 29, 36, 45} Set #3 = {-11, -8, -3, 4, 13} Set #4 = {22, 31, 38, 43, 46} That last set has the "spacings" in the reverse order. That doesn't matter. As long as the set of spacings is the same, the SD is the same. All four of these sets have the same SD. If you think of each set as a set of five dots on the number line, notice that each set is the same pattern of dots--we could just slide the pattern up or down the number line, or flip it around & slide it in the case of set 4. sets on number line.png Now, consider the two sets given in this statement: Set A = {n, 2, 2, 2} and set B = {n, n, n, 2}. Let say the distance between n and 2 is D = |n - 2|. In both sets, we have three dots in one place and one dot that is D units away from those three. Thus, we have the same "spacings," the same pattern of dots, in both sets. Both sets have the same S.D. We can give a definitive "yes" to the prompt question. Because we have enough information to give a definitive answer, this statement, alone and by itself, is sufficient . OA = (B) Does all this make sense? Mike :-)

nks2611 · Answer

the answer should be B 
although C is tempting but if we put any value in place of n then the s.d. will always be the same.

guialain · Answer

Very nice one.
It shows that SD measure the actually the "Dispersion" around the average value of the items.

(1)- Not sufficient
(2)- Sufficient. Can be done by trying different value of n.
Below is a formula approach

flippedeclipse · Answer

Tough question. Took some time to wrap my head around this.

Statement 1 gives us very little info, so insufficient.

Statement 2 requires some visualizing of standard deviations. Let's take a value for n as 10, just as an example.

For Set A, if n is 10, the mean of the set is 4. For Set B, mean is 8.

Standard deviation measures the distance from the mean. For Set A, these distances end up being:
   Datapoint 
 Distance from Mean 
 
  2 
 2 
 
  2 
 2 
 
  2 
 2 
 
  10 
 6

For Set B, these distances end up being:
   Datapoint 
 Distance from Mean 
 
  10 
 2 
 
  10 
 2 
 
  10 
 2 
 
  2 
 6

Standard deviation cares about the distance from the mean for its calculation, not the datapoint value itself. Since the distances from the mean are the same here, it'll result in the same value for standard deviation. The answer to "Are the standard deviations of Set A and Set B the same?" is a definitive yes for Statement 2. Our answer is B.

Are the standard deviations of set A and set B the same? 1) n=6 2) S

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GMAT Data Sufficiency (DS) Questions

Are the standard deviations of set A and set B the same? 1) n=6 2) S

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