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# Is the standard deviation of the salaries of Company Y s

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Senior Manager
Joined: 28 Jun 2007
Posts: 276
Is the standard deviation of the salaries of Company Y s  [#permalink]

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08 Sep 2007, 13:14
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Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?

(1) The average (arithmetic mean) salary of Company Y’s employees is greater than the average salary of Company Z’s employees.

(2) The median salary of Company Y’s employees is greater than the median salary of Company Z’s employees.
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Joined: 10 Jun 2007
Posts: 1303
Re: DS - Set 2, Math 3  [#permalink]

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08 Sep 2007, 14:34
2
gluon wrote:
Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?

(1) The average (arithmetic mean) salary of Company Y’s employees is greater than the average salary of Company Z’s employees.

(2) The median salary of Company Y’s employees is greater than the median salary of Company Z’s employees.

Straight E

(1) say y = {3,3,3}, z = {1,1,1)
Same SD, but Avg(y) > Avg(z)
say y = {1,3,5}, z = {1,1,1)
Different SD, but Avg(y) > Avg(z)
INSUFFICIENT

(2) Using the same case above, INSUFFICIENT

Together, still same case.
Director
Joined: 03 May 2007
Posts: 763
Schools: University of Chicago, Wharton School
Re: DS - Set 2, Math 3  [#permalink]

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27 Sep 2007, 22:28
gluon wrote:
Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?

(1) The average (arithmetic mean) salary of Company Y’s employees is greater than the average salary of Company Z’s employees.
(2) The median salary of Company Y’s employees is greater than the median salary of Company Z’s employees.

E. we need number of emplyoees and their salary dist.
SVP
Joined: 29 Mar 2007
Posts: 2326
Re: DS - Set 2, Math 3  [#permalink]

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27 Sep 2007, 23:05
1
gluon wrote:
Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?

(1) The average (arithmetic mean) salary of Company Y’s employees is greater than the average salary of Company Z’s employees.

(2) The median salary of Company Y’s employees is greater than the median salary of Company Z’s employees.

E.

Std Deviation is essentially the distance from the mean. It can also be somewhat thought of as the spread between the various numbers.

Ex/ 1,2,3,4,5. Mean is 3, and so is the median. STD is equal to 1.

There is a very tedious method to figure out the std deviation, buts its unlikely ul be tested on it.

For S1: this doesnt tell us the std dev's are different.

S2: same thing.

For both and for either statement you can make up two sets:

Set Y and Set Z

Y: 2,3,4,5,6

Z: 1,2,3,4,5. Both mean and median are greater in set Y. But std deviation is the same.

You can create many sets where the std D is different.
Math Expert
Joined: 02 Sep 2009
Posts: 55729
Re: DS - Set 2, Math 3  [#permalink]

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11 Sep 2010, 23:33
2
2
gluon wrote:
Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?

(1) The average (arithmetic mean) salary of Company Y’s employees is greater than the average salary of Company Z’s employees.

(2) The median salary of Company Y’s employees is greater than the median salary of Company Z’s employees.

This one is straight E. No need to look for examples.

"Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values."

We know only that mean(Y)>mean(Z) and median(Y)>median(Z) - absolutely useless info to compare SD's.

But still if you need an example:
Consider company Y to have one employee with a salary of \$10, so SD(Y)=0 (if Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero) and company Z to have two employees with a salaries of \$1 and \$2, so SD(Z)>0: mean(Y)>mean(Z) and median(Y)>median(Z) but SD(Z)>SD(Y)=0;

Now, consider company Y to have two employees with a salaries of \$10 and \$11, so SD(Y)>0 and company Z to have one employee with a salary of \$1, so SD(Z)=0: mean(Y)>mean(Z) and median(Y)>median(Z) but SD(Y)>SD(Z)=0.

For more on standard deviation check:
SD chapter of Math Book: math-standard-deviation-87905.html

Hope it helps.
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Joined: 06 Nov 2014
Posts: 1877
Re: Is the standard deviation of the salaries of Company Y s  [#permalink]

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20 Jul 2015, 02:32
1
Is the standard deviation of the salaries of Company Y’s employees greater than the standard deviation of the salaries of Company Z’s employees?

To calculate the standard deviation we need the mean and each of the values in the set.

(1) The average (arithmetic mean) salary of Company Y’s employees is greater than the average salary of Company Z’s employees.
We don't have information on the salary values of the companies.
(2) The median salary of Company Y’s employees is greater than the median salary of Company Z’s employees.
We don't have information on the mean salaries of the companies.

We don't have useful information from either statement individually or combined. E
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Re: Is the standard deviation of the salaries of Company Y s  [#permalink]

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19 Mar 2019, 14:52
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Re: Is the standard deviation of the salaries of Company Y s   [#permalink] 19 Mar 2019, 14:52
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