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# Both A and B are sets of 5 integers. Which one's standard

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Both A and B are sets of 5 integers. Which one's standard [#permalink]  30 Nov 2004, 05:33
Both A and B are sets of 5 integers. Which one's standard deviation is bigger?
(1) A's range is bigger than B's range.
(2) A's average is bigger than B's average.
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By plugging in numbers, I got E
Consider 2 sets:
A={1-4-7-10-13}
B={0-3-6}
Both set's standard deviation are same with A's average being larger than B's average. You can see here that the range for A is also larger than the range for B. Hence, both condition 1 and 2 are satisfied. However, it is impossible to determine the SD because let's say that you include a number within the range of 1 to 13, the SD will be smaller for A than B. On the other, if you add a number that is beyond the max value of 13, say 1000, the SD will be much more higher for A than it would be for B. Therefore, it is inconclusive.

PS. SD is equal to the sum of all the deviations from the mean
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hategmat wrote:
Both A and B are sets of 5 integers. Which one's standard deviation is bigger?
(1) A's range is bigger than B's range.
(2) A's average is bigger than B's average.

I agree with Paul. The answer is E.

The more you know about standard deviation, the more this can just be a thought experiment for you. The standard deviation of any list is not dependent on the average, but on the deviation of the numbers from the average. So knowing that two lists have different averages doesn't say anything about their standard deviation - different averages can have the same SD.

Same thing with range. If all the numbers are close, but one is way off, the range will be large but the SD will be small. Alternatively, if they are all very different from the average, the SD will be high, regardless of the range.

So all that together still doesn't tell us anything, and the answer is E.

One more note about range: If the range is 0, then the SD must also be 0, because there is no variance whatsoever. That's a good thing to tuck into your toolbox for a rainy day.
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