Princeton Review
"1,012 GMAT Practice Questions"
Standard Deviation Drill (page 239)
-data sufficiency question
8. If set S consists of an odd number of even integers that have a normal distribution, what is the standard deviation of set S?
(1) The mean of set S is 4.
(2) The median of set S is 4.
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[spoiler]Book Answer: (C)[/spoiler]
"Statement (1) is not sufficient because it tells you the mean, but nothing about the other numbers in the set. You could Plug In two sets of numbers for the set and get two different standard deviation. Eliminate choices (A) and (D). Statement (2) is also insufficient. Again, you could Plug In two sets of numbers to get two different standard deviations. Eliminate choice (B). Combining the two statements tells you that the numbers in set S are consecutive, because in a consecutive set of numbers, the mean equals the median. If the numbers are consecutive, even integers and the mean is 4, you know that the standard deviation is 2."
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I agree that the only possible choices are (C) or (E). But! Why must the set be consecutive? For example, consider this set of even numbers,
{4, 6, 10, 12, 18}
The mean and median are both 10 yet the set is not consecutive. Correct? I thought for a set to be consecutive there had to be even spacing between numbers that were in ascending or descending order. Like:
{3,4,5,6,7,8} or {-5,-4,-3,-2,-1,0,1,2,3}
Are the following considered consecutive number sets?
{5,10,15,20,25} or {-80, -84, -88, -92}
One last question:
Assume that the set of numbers in the book question is consecutive with a mean of 4, just like the author concluded in the answer. Why must the standard deviation be 2? The set could be ANY size. The only restrictions are that there are "an odd number of even integers." If there were 25 even, consecutive integers with a mean of 4, the standard deviation would surely not be 2! Therefore the information is insufficient and the answer is choice (E).
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Did I do everything right? Can you please explain consecutive number sets more clearly? Did I come to the correct conclusion? Thank you!
"1,012 GMAT Practice Questions"
Standard Deviation Drill (page 239)
-data sufficiency question
8. If set S consists of an odd number of even integers that have a normal distribution, what is the standard deviation of set S?
(1) The mean of set S is 4.
(2) The median of set S is 4.
--------------------------------------------------------------------------------
[spoiler]Book Answer: (C)[/spoiler]
"Statement (1) is not sufficient because it tells you the mean, but nothing about the other numbers in the set. You could Plug In two sets of numbers for the set and get two different standard deviation. Eliminate choices (A) and (D). Statement (2) is also insufficient. Again, you could Plug In two sets of numbers to get two different standard deviations. Eliminate choice (B). Combining the two statements tells you that the numbers in set S are consecutive, because in a consecutive set of numbers, the mean equals the median. If the numbers are consecutive, even integers and the mean is 4, you know that the standard deviation is 2."
--------------------------------------------------------------------------------
I agree that the only possible choices are (C) or (E). But! Why must the set be consecutive? For example, consider this set of even numbers,
{4, 6, 10, 12, 18}
The mean and median are both 10 yet the set is not consecutive. Correct? I thought for a set to be consecutive there had to be even spacing between numbers that were in ascending or descending order. Like:
{3,4,5,6,7,8} or {-5,-4,-3,-2,-1,0,1,2,3}
Are the following considered consecutive number sets?
{5,10,15,20,25} or {-80, -84, -88, -92}
One last question:
Assume that the set of numbers in the book question is consecutive with a mean of 4, just like the author concluded in the answer. Why must the standard deviation be 2? The set could be ANY size. The only restrictions are that there are "an odd number of even integers." If there were 25 even, consecutive integers with a mean of 4, the standard deviation would surely not be 2! Therefore the information is insufficient and the answer is choice (E).
--------------------------------------------------------------------------------
Did I do everything right? Can you please explain consecutive number sets more clearly? Did I come to the correct conclusion? Thank you!
