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Is the standard deviation of ages of students in class A [#permalink]

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18 Feb 2004, 09:50

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
100% (01:32) wrong based on 1 sessions

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Class..............Average Age........# of Students A..................15 years.....................6 B..................16 years.....................12

Is the standard deviation of ages of students in class A greater than the standard deviation of the ages of students in class B?

(1) The maximum difference between the ages of any two students in class A is 1 year.

(2) No student in class B is more than 6 months older than any other student.

C would be the answer
From 1) St. dev. for A is 1 yr. not suff. since we don't know the st. dev. of B
From 2) st. dev. for B is 1/2 yr. not suff. since we don't know the st. dev. of A

Both together we know their relative st. dev. and thus conclude that B's st. dev. is less. St. dev. is a measure of dispersion from the mean. Therefore, the averages of 15 for A and 16 for B have no incidence in selecting an answer regarding st. dev. _________________

Standard deviation indicates the spread of data points around the mean. So the stem is asking whether the points in data set A cluster further away from the mean (on average) than the points in data set B.

Looking at the statements:

1) tells us that 1 is the maximum difference between the ages of any two students. This means that some students may be under 15, and some over 15, but since we need a final average that is exactly 15 years, the ages "under" will have to balance the ages "over. For example, you could have 3 students at 14.5 and 3 students at 15.5. But you could also have all students at exactly 15, which yields a st. dev. of 0.

2) is the same as 1, but with a range of 6 months max. Again, it could be 6 students at 3 months under 16, and 6 students at 3 months over 16. In this case, st. dev is > 0. But again, all ages could be exactly 16.

Since there is no information about the actual spread in either statement, and we only know that the range does not exceed a certain amount, the ans is E.

Standard deviation indicates the spread of data points around the mean. So the stem is asking whether the points in data set A cluster further away from the mean (on average) than the points in data set B.

Looking at the statements:

1) tells us that 1 is the maximum difference between the ages of any two students. This means that some students may be under 15, and some over 15, but since we need a final average that is exactly 15 years, the ages "under" will have to balance the ages "over. For example, you could have 3 students at 14.5 and 3 students at 15.5. But you could also have all students at exactly 15, which yields a st. dev. of 0.

2) is the same as 1, but with a range of 6 months max. Again, it could be 6 students at 3 months under 16, and 6 students at 3 months over 16. In this case, st. dev is > 0. But again, all ages could be exactly 16.

Since there is no information about the actual spread in either statement, and we only know that the range does not exceed a certain amount, the ans is E.

Good point mate .. I missed while reading the question and answered C but after readin your explanation I understand why should be E

Cheers

gmatclubot

Re: DS - Standard Deviation
[#permalink]
06 May 2010, 06:10

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