If a certain sample of data has a mean of 20.0

[divya8486]

If a certain sample of data has a mean of 20.0 and a S.D of 3.0,which of the following values is more than 2.5 S.D. from the mean?
a.12.0
b.13.5
c.17.0
d.23.5
e.26.5

The correct answer is A.
I used this strategy. When SD is 2.5 from the mean,it can be that 20+2.5(3.0) or 20-2.5(3.0). When i calculated,i got 27.5 for the first and 12.5 for the second. Hence i ruled out c,d,e since they were away from either of the answers.I seleceted b since 13.5 is more than 2.5 times SD.Could u please tell me where i went wrong?

[RonPurewal]

If a certain sample of data has a mean of 20.0 and a S.D of 3.0,which of the following values is more than 2.5 S.D. from the mean?
a.12.0
b.13.5
c.17.0
d.23.5
e.26.5

The correct answer is A.
I used this strategy. When SD is 2.5 from the mean,it can be that 20+2.5(3.0) or 20-2.5(3.0). When i calculated,i got 27.5 for the first and 12.5 for the second. Hence i ruled out c,d,e since they were away from either of the answers.I seleceted b since 13.5 is more than 2.5 times SD.Could u please tell me where i went wrong?

ah, yes.

this is one of those language ambiguities that, annoyingly enough, only seems to trouble non-native speakers of english. it's rare for such things to happen on the quant side of the exam, but they do.

here's the story:

you're processing the words as
more than ... 2.5SD away from the mean

when you should be processing them as
more than 2.5SD ... away from the mean

in other words, the distance from the mean must be more than 2.5SD, in either direction. in this particular problem, then, this means that the value in question must be either more than 27.5 (as you figured) or LESS than 12.5.
this leaves (a).

incidentally, you can prove that your interpretation isn't the desired one by looking at the answer choices: all of (b), (c), (d), and (e) are greater than 12.5, so "greater than 12.5" clearly doesn't work as a criterion.

--

make sure you realize this as a takeaway: if they say "more than x away from y", this means that the distance from y must be more than x, in either direction.
i can understand why you may have interpreted the question the way you did, but ... that's not the convention.
now you know.