Veritas - Most Increase SD

For the set {2, 2, 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most
increase the standard deviation?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

For the purposes of the GMAT, we need not involve the actual standard deviation. Instead, it's sufficient to think of Standard Deviation as the Average Distance from the Mean. This is a convenient way to handle most standard deviation questions on the GMAT.

In this case, the mean = 3.5
When we check the answer choices, answer choice A is furthest from the mean (3.5).
So, A is the correct answer.

Here are two free videos that cover everything you need to know about standard deviation on the GMAT:
- https://www.gmatprepnow.com/module/gmat- ... ics?id=806
- https://www.gmatprepnow.com/module/gmat- ... ics?id=809

Here are a few more practice questions where we can apply the concept of "average distance from the mean" as an approximation for Standard Deviation:
- https://www.beatthegmat.com/standard-dev ... 74384.html
- https://www.beatthegmat.com/standard-dev ... 69584.html
- https://www.beatthegmat.com/range-and-sd-t89159.html

Cheers,
Brent

Hi nikhilgmat31,

The GMAT will never ask you to actually calculate a Standard Deviation; instead, you're expected to understand the general concepts behind the subject (and you'll be asked a question - likely just 1 on Test Day - about that general knowledge). In real basic terms, SD is about how 'spread out' a group of numbers is. The 'closer' the numbers are together, the smaller the SD; the 'further apart' the numbers are, the higher the SD.

From this group of numbers, you should see (rather quickly) that there are 2 of each integer and 1 unknown. The question asks for the value of that unknown that will MOST increase the SD of the group. Mitch and Brent have both properly explained how to get to the correct answer, so I won't rehash that work here. Instead, here's how you can eliminate answer choices for NOT creating the highest SD.

With the 8 integer values that we're given, the average is 3.5 (the values 'balance' around that number). Including another 3 or another 4 would have the SAME effect on the SD (they would both introduce a value that is the SAME 'distance' from the average), so neither of those answers could create the highest SD (the net result would be the SAME). That same pattern occurs when we consider including another 2 or another 5 - each of those values is the SAME distance from the average, so each of their impacts on the SD would be the SAME. Thus, neither of those could create the highest SD.

There's only one answer remaining...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich