Word Problems 5th Ed. Page 63 #9

[samanthakfranklin]

The question states:

{9,12,15,18,21}

Which of the following pairs of numbers, when added to the set above, will increase the standard deviation of the set?

I. 14, 6
II. 9, 21
III. 15, 100

(A) II only (B) III only (C) I and II (D) II and III (E) I, II, III

I calculated the mean to be 15. And I selected answer choice (B) because 100 would cause the spread to greatly increase.

But according to the solution the answer choice is (D). I think I might be missing something here as I'm not sure how adding 9, 21 would increase the SD if they are already included in the original set.

Would appreciate any extra information/help on this.

Thanks in advance!

[RonPurewal]

Read this post, which contains absolutely everything you'll need to know about the standard deviation on this exam:

post86007.html#p86007

Once you've read that --
Among all existing data points, 9 and 21 are farthest from the mean. Therefore, if you duplicate those values, you're increasing the "spread" of the set.

[RonPurewal]

Also, there's one aspect of this problem that is somewhat unsavory: namely, the word "add" is ambiguous.

Here, "add" is used in the sense of "append onto the existing list, creating a list with more entries".
The problem, of course, is that "add" can also mean, well, add.

That's not a possibility in this problem, because adding a constant value to every number in a set will leave the SD exactly the same as it was before. (If that happens, the "spread" is no more -- and no less -- than it was before. It's the same.)
So, if "add" meant literally add (to each of the individual numbers), the answer to the problem would be "None".

But, if you're solving a problem on the official test, look for clues so that you're certain which kind of "adding" we're talking about. They could reasonably ask about either one -- adding a constant value or appending extra numbers to the list -- so, be careful.