A researcher computed the mean, the median, and the...

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue Dec 19, 2017 10:45 am

A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?

A) The mean only
B) The median only
C) The standard deviation only
D) The mean and the median
E) The mean and the standard deviation

The OA is D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Dec 19, 2017 10:45 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue Dec 19, 2017 11:41 am

swerve wrote:A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?

A) The mean only
B) The median only
C) The standard deviation only
D) The mean and the median
E) The mean and the standard deviation

The OA is D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.

If you do this in the following way, you don't even need to know what standard deviation means.

Assume two scores, each 0. So the mean is 0 and the median is 0.

Add 5 to each, therefore the new scores are 5 and 5. The median is 5 and the mean is also 5.

So you know that both the mean and median changed. The only answer that fits is D

And BTW, since there can only be one correct answer, you can safely infer that standard deviation did not change.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Dec 20, 2017 12:04 pm

Hi swerve,

regor60's approach to TEST VALUES to prove the correct answer is 'spot on', so I won't rehash any of that here. Instead I'll add an additional note about Standard Deviation. While the GMAT will never ask you to actually calculate S.D., you will be expected to understand the basic ideas behind S.D. In simple terms, S.D. is really about how 'spread out' a group of numbers is - the closer the numbers are together, the smaller the S.D.; the farther apart the numbers are, the higher the S.D. If all of the numbers are the SAME, then the S.D. = 0.

If you have a group with of numbers with an S.D. of X, and you increase all of the number by the same VALUE (in this case, increasing each number by 5), then the spread will NOT change, so the S.D. will not change either.

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

Contact Rich at [email protected]

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