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Hi guys!

Q) 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

We need to know the mean or average to answer this question.

I. Gives the mean of both companies, since the mean of B is the range of B, the spread (STD) of the salary data of B is narrow compared with A. Sufficient.

II. Gives the highest salary of A & B, thus given the range the lowest salary of both companies can be found BUT we are interested in the mean to answer the question and this stem does not provide that information. Insufficient.

What we need is the average/arithmetic mean. This is provided to us in statement 1. This, together with, the range from the question stem is enough to answer the question.

Q) 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

support ur answers with reasoning.

Thanks Saurabh Malpani

the value of SD depends upon number of observations and the value of fluctuations i.e. we can say range. all other things being equal, the higher the range, the greater the SD. similarly, higher the number of observations, lower the SD.

from i, it can be said that these two companies have same mean, therefore the company A has higher SD over company B.

Q) 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

Is there a typo in the question? If you combine statements 1 and 2, you have
1) average of A = average of B = 30,000
2) Lowest salary of A = lowest salary of B = 30,000

How can you have an average of 30,000 if the lowest number is 30,000 and the highest is 90,000 or 60,000. the average has to be greater than 30,000

(E).
Though we are given th mean, the range and the smallest as well as laargest salary, i think those are not sufficient to compute the standard deviation considering we do not
1. the number of employees each company has
2. the specific salary of each employee (data point). REcall that deviation is the measure of variation between the mean and each data point.

i could be wrong though because this is GMAT so i look forward to the OA

Q) 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

Is there a typo in the question? If you combine statements 1 and 2, you have 1) average of A = average of B = 30,000 2) Lowest salary of A = lowest salary of B = 30,000

How can you have an average of 30,000 if the lowest number is 30,000 and the highest is 90,000 or 60,000. the average has to be greater than 30,000

Hi gayathri, The difference between this question and the one you provided the link to is that in this one, you are provided with the range and the SAME averages. At least, this is what you get as piece of information from stem and A. When you have SAME averages AND the ranges are given, you can find the SD around the mean. Consider my attachment below. A says that the average is 30, represented by the red square. The range is represented by the size of the box; 60 for CorpA and 30 for CorpB. Now, knowing that the average is 30 AND the range is 60 for A, we know that the SD for CorpA is then 30(+/-30 around the mean). For B, since the average is 30 AND the range is 30, we know that the SD is then 15(+/-15 around the mean). Hence, SD for CorpA is larger than SD for CorpB. A is sufficient.

Looking at only statement B, All we know are the highest salaries AND the range. The range being represented by the boxes does not change. What changes here is that we have the right hand side of the boxes touching 90 for CorpA and the 60 for CorpB. Their respective left hand sides will then be at 30 for both Corporations. However, does that mean that the SD will be +/-30, as previously explained, for CorpA and +/-15 for CorpB? Answer is NO because even the ranges are given, we do not know the mean, or in other words, the distribution of the individual data within that given range. Let's say we have a company of 3 employees for CorpA. The first one makes 30 and the second one makes 90. If the third employee makes 60, then the average will be 60 for CorpA but if the third employee makes 30, then the average will be (30+30+90)/3 = 50! Hence, the average can fluctuate because it is not given. If the average fluctuates, we will not know what the SD is for sure. So B is not sufficient.

Re-read carefully the link that you gave me and you will see that in that question, although the ranges are given, the averages are NOT same so it is not possible to compare the two and come to a conclusion. SD is one of the tough concepts to explain but which you have to read about on your own time in some college math or stats books. I would say that this is a highly likely GMAT question so make sure you understand the nuance between the "creative" ways in which ETS can ask you this.
_________________

Best Regards,

Paul

Last edited by Paul on 21 Jan 2005, 12:02, edited 1 time in total.

Hmmm, I just noticed you cannot put attachments anymore. I will wait for the server transfer to be done and will post my attachment to the previous message to ease your understanding
_________________

I donâ€™t see why A is the OA. I totally agree with Folaa3, standard deviation gives a measure of how the data is arranged around the mean.

For Co. A the range is 60K, but it could be that there is only 1 salary 30K less than the mean (the sandwich boy, or the janitor) and 1 salary 30K greater than the mean (the CEO), but then lots of employees can have the salary exactly on the mean or very close to it. Then the STD will be very small. For Co. B, it could happen than the salaries are scattered around with lots of employees with salaries quite far away from the mean (Lots of low salaries and lots of high salaries, but few around the mean). Then Co. B will have a relatively large STD, bigger than Co. A.

But it could happen the opposite, salaries in A scattered and far from the mean, and salaries for B very close to the mean.

Letâ€™s assume companies have 10 employees:

salaries for A (in â€˜000s): 15, 43, 44, 44, 45, 45, 46, 46, 47, 75.
Range 60, average: 45
STD for A: 14.18

Salaries for B (in â€˜000s): 25, 25, 26, 26, 27, 52, 53, 54, 54, 55
Range: 30, average: 38.11
STD for B: 14.63

But:

salaries for A (in â€˜000s): 15, 25, 30, 35, 45, 45, 55, 60, 65, 75.
Range 60, average: 45
STD for A: 19.00

Salaries for B (in â€˜000s): 25, 27, 29, 30, 31, 32, 35, 40, 50, 55
Range: 30, average: 35.4
STD for B: 9.99

(STD calculated using the Windows XP calculator)

Statement 2 doesnâ€™t change anything, so I think the answer is E. Can anybody explain why is A, and give examples, please?

I thought so as soon as looked at the question.
I pick E.
My reasoning is:
Regardless of what the range is, we have no information about how the salaries are clustered around the mean in the two companies.
It is possible the two salaries, the largest and the smallest could be far away from the mean, but rest of the salaries could be closer to the mean, thereby reducing the SD.

Guys, can we discuss this one a bit more? Letâ€™s assume companies have 10 employees:

salaries for A (in â€˜000s): 15, 43, 44, 44, 45, 45, 46, 46, 47, 75. Range 60, average: 45 STD for A: 14.18

Salaries for B (in â€˜000s): 25, 25, 26, 26, 27, 52, 53, 54, 54, 55 Range: 30, average: 38.11 STD for B: 14.63

But:

salaries for A (in â€˜000s): 15, 25, 30, 35, 45, 45, 55, 60, 65, 75. Range 60, average: 45 STD for A: 19.00

Salaries for B (in â€˜000s): 25, 27, 29, 30, 31, 32, 35, 40, 50, 55 Range: 30, average: 35.4 STD for B: 9.99

(STD calculated using the Windows XP calculator)

Statement 2 doesnâ€™t change anything, so I think the answer is E. Can anybody explain why is A, and give examples, please?

A.

Although your points are valid, if you start putting numbers you get property something like this:

"For data with approximately the same mean, the greater the range, the greater the standard deviation. "

In the examples you gave, you missed the point that A says "mean is same"

artabro wrote:

For Co. B, it could happen than the salaries are scattered around with lots of employees with salaries quite far away from the mean (Lots of low salaries and lots of high salaries, but few around the mean). Then Co. B will have a relatively large STD, bigger than Co. A.

In this case, the mean itself would be larger for Co B.