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08 Sep 2007, 13:14
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E
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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.
(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.
11 Sep 2010, 23:33
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gluon
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
PS questions on SD: ps-questions-about-standard-deviation-85897.html
DS questions on SD: ds-questions-about-standard-deviation-85896.html
Hope it helps.
General Discussion
08 Sep 2007, 14:34
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gluon
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.
