## Is the standard deviation of set Q equal to 0?

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### Is the standard deviation of set Q equal to 0?

by AAPL » Tue Feb 11, 2020 5:49 am
Economist GMAT

Is the standard deviation of set Q equal to 0?

1) The average (arithmetic mean) of set Q is equal to the greatest number in Q.
2) The mean of the set Q is equal to the greatest number in Q.

OA A

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### Re: Is the standard deviation of set Q equal to 0?

by Ian Stewart » Tue Feb 11, 2020 1:33 pm
AAPL wrote:
Tue Feb 11, 2020 5:49 am
Economist GMAT

Is the standard deviation of set Q equal to 0?

1) The average (arithmetic mean) of set Q is equal to the greatest number in Q.
2) The mean of the set Q is equal to the greatest number in Q.

OA A
I don't understand the question. First, in math, a "set" cannot contain repeated elements, but the "set" in this question clearly does, so they're misusing terminology.

The standard deviation of a list is zero when every element in the list is the same. If the largest value in a list is equal to the mean of the list, then every element in the list is the same. You can see that in many ways -- for example, imagine the largest value in a list is 25, and the average of the list is 25. Take all the 25's out of the list. Removing exactly average things from a list doesn't affect the average, so our new list will also have an average of 25, but we've taken out all of the largest values, so every remaining value must be less than 25. But then we have a list with an average of 25, with no value equal to or greater than 25. That's impossible, because everything can't be below average. So it must be true that after removing all of the 25's we've removed every value. So Statement 1 is sufficient. For GMAT purposes, Statement 2 says exactly the same thing as Statement 1 (if a GMAT question says "the mean", it means "the arithmetic mean" only and not any other kind of mean) so it's also sufficient. That's why I don't understand the question, since the OA is given as "A" -- the answer is D.
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