In two companies, the range of the member's salary is

Question

1: In two companies, the range of the member's salary is different. The range of company A is 60,000 and of B, is 30,000. Which company's deviation is greater?

1) The two companies have a same average salary $30,000. 
2) The highest salary of A is 90,000. The highest salary of B is 60,000

x2suresh · Answer

I will go for E.

Atleast we need no of members in each comapny...

sondenso · Answer

E.

only the range and the mean says nothing about the STD

IanStewart · Answer

This question doesn't make any sense. If a finite set has a nonzero range, the set must contain at least one value which is greater than the average, and one that is less than the average. If the average salary at company X is $30,000, and the range is $60,000, it's impossible for the highest salary to be $90,000. The only way this would be possible is if an infinite number of employees making $30,000 per year worked for the company. Where is the question from?

GMAT TIGER · Answer

It was discussed with some nice concepts on STD here: 7-p72619?t=12564&hilit=deviation#p72619

IanStewart · Answer

Interesting- there's a lot of bad math in that thread, but eventually they land on the right answer. A few people posting in that thread seem to think that 'the larger the range, the larger the standard deviation', which is nonsense. One set can easily have a larger range, but a smaller standard deviation, than another set. For example:

{0,51,51,51,51,51,51,51,51,102}

has a larger range, but a smaller standard deviation, than this set:

{0, 0, 0, 0, 0, 100, 100, 100, 100, 100}

{0,51,51,51,51,51,51,51,51,102}

has a larger range, but a smaller standard deviation, than this set:

{0, 0, 0, 0, 0, 100, 100, 100, 100, 100}

GMAT TIGER · Answer

Ian,

This a place for practice and learning. Some might make mistake in this process. Nobody is perfect. That is ok until he or she is nice and respectful to others. But you, as a moderator, should be careful while chosing the words that are ofending. "Nonesense" doesnot fit to moderators.

Hope you will refrain from using such ofending words.

IanStewart · Answer

GT - I mean the word in its literal meaning: 'non-sense', as in 'does not make sense'. You linked to a four year old thread in which more than one poster made some forceful and very misleading claims about the relationship between range and standard deviation. It is precisely because this forum is a place for learning that I wanted to leave no room for ambiguity in clarifying what is and is not true about that relationship; otherwise some might read part of the thread to which you linked, and then make mistakes on their GMAT because of the misinformation found there.

And I have no more affiliation with gmatclub than anyone else participating on this forum; someone - I don't know who - apparently made me a moderator, but that was not by my choosing.

And I have no more affiliation with gmatclub than anyone else participating on this forum; someone - I don't know who - apparently made me a moderator, but that was not by my choosing.

scthakur · Answer

Without looking at the posts on the thread that GT has posted, I picked A for the following reason.

1. The question is asking about the comparison of two SDs and not their absolute values. Hence, knowing each member of these sets is not required. 
2. Just range will not be sufficient to answer the question. However, if the average and range are known, one gets an idea of the spread of distribution curve (and hence the idea of SD). This much information is sufficient to compare the SD of two sets.

GMAT TIGER · Answer

The question is not a aproperly designed as some othe members pointed in the original post particularly for statement 2.

Avg = 30,000.00
Range = 60,000.00
Highest = 90,000.00 not possible.

Sorry for my posting the question without verifying its assumptions. 
However the OA is said to be E...

In two companies, the range of the member's salary is

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards