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# CLASS AVERAGE AGE NO.OF STUDENTS A 15 YEARS 6 B 16 YEARS 12

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CLASS AVERAGE AGE NO.OF STUDENTS A 15 YEARS 6 B 16 YEARS 12 [#permalink]  25 Mar 2011, 09:48
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Q))
CLASS AVERAGE AGE NO.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 age of students in class B ?

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

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

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
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Re: KAPLAN TEST QUES [#permalink]  25 Mar 2011, 10:06
1
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Q))
CLASS AVERAGE AGE NO.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 age of students in class B ?

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

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

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

(1) The difference between the ages of any two students in class A is always more than 1 year.
INSUFFICIENT. No mention about class B here.

(2) No student in class B is more than 6 months older than any other student.
INSUFFICIENT. No mention about class A here.

Combing both and assuming that both classes have at least 2 students;
We can see that the standard deviation will increase with every student added for class A and the the deviation will decrease with every student added to class B.

Maximum standard deviation for class B can be somewhere around 0.25 years or 3 months and the minimum standard deviation of class B will be somewhere around 0.5 years.

Thus Std Dev(A) > Std Dev(B)

Sufficient.

Ans: "C"
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Re: KAPLAN TEST QUES [#permalink]  25 Mar 2011, 10:07
1
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Q))
CLASS AVERAGE AGE NO.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 age of students in class B ?

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

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

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

C.

Statement 1 alone is not enough. It doesn't give any indication what the differences of ages in class B are.
For example, everyone in class B could be exactly the same age, or everyone in class B could be 2 years apart.

Statement 2 alone is not enough. It doesn't give any indication what the difference of ages in class A are.
Everyone in class A could be exactly the same age, or everyone in class A could be 2 years apart.

If you combine them, you know that A has a significantly larger standard deviation in ages.
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Re: KAPLAN TEST QUES [#permalink]  26 Mar 2011, 18:09
1
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A - a1, a2, a3,a4,a5,a6

Total A = 90

a1-a2 > 12 months and so on, but no information about B, so insufficient.

B - b1,b2,b3,b4,b5... b12

Total B = 192

b1-b2 <= 6 month , but no information a bout A, so insufficient

From (1) and (2) together, the difference between elements of set A is > the difference between elements of Set B, and the denominator in A is < the denominator in set B for the Std Dev formula.

=> Std Dev A > Std Dev B

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Re: KAPLAN TEST QUES [#permalink]  26 Mar 2011, 19:21
standard deviation is the underroot of the (sum of squares of the difference b/w the quantity and the mean divided by the no of quantities).
now since the statement 1 doesnt mentions abt B and stat. 2 doesnt mentions abt A. hence they both are insufficient.

on combining the two statements do we get the full information to make a comparison?
YES.

also keep in mind that the diff b/w the mean and the quantity in B wud always be less than 1 and therefore its square wud be much more smaller.
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Re: KAPLAN TEST QUES [#permalink]  04 Nov 2011, 06:52
Thanks for the explanations.
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Re: CLASS AVERAGE AGE NO.OF STUDENTS A 15 YEARS 6 B 16 YEARS 12 [#permalink]  04 Jan 2012, 02:28
Question: Is SD(A) > SD(B)?

Statement 1: No mention of students in class B. Thus INSUFFICIENT

Statement 2: No mention of students in class A. Thus INSUFFICIENT

Combining the two statements, we can see that the difference between the ages of two students in class A is considerably larger than the difference between the ages of any two students of class B.
As we know that SD is a measure of the compactness within the elements of a set, we can infer that the elements of Set A are more dispersed than are the elements of Set B. Thus, we know that SD (A) > SD (B). SUFFICIENT.

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Re: CLASS AVERAGE AGE NO.OF STUDENTS A 15 YEARS 6 B 16 YEARS 12 [#permalink]  04 Jan 2012, 02:55
C.. Appreciate Fluke suggestion
Re: CLASS AVERAGE AGE NO.OF STUDENTS A 15 YEARS 6 B 16 YEARS 12   [#permalink] 04 Jan 2012, 02:55
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