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Intern  Joined: 31 Oct 2007
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Is the standard deviation of ages of students in class A greater than  [#permalink]

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4 00:00

Difficulty:   15% (low)

Question Stats: 81% (01:15) correct 19% (01:17) wrong based on 114 sessions

### HideShow timer Statistics 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.

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GMAT 1: 750 Q50 V40 Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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C

$$SD_A>\sqrt{12}$$ and $$SD_B<=\sqrt{6}$$

So, $$SD_A>\sqrt{12}>\sqrt{6}>=SD_B$$

$$SD_A>SD_B$$
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GMAT 1: 750 Q50 V40 Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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It should be 12 and 6 instead of sqr(12) and sqr(6), but it does not influence on reasoning.
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Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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OA is C

My math concepts around statistics and standard deviation are weak. Can you share some resources for improvement?
VP  Joined: 04 May 2006
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Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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zeenie wrote:
walker wrote:
C

$$SD_A>\sqrt{12}$$ and $$SD_B<=\sqrt{6}$$

So, $$SD_A>\sqrt{12}>\sqrt{6}>=SD_B$$

$$SD_A>SD_B$$

Yep. C it is

If More detail is better! thanks!
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GMAT 1: 750 Q50 V40 Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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1
1
sondenso wrote:
If More detail is better! thanks!

Thanks you, you force me to think more carefully fast (guessing) way: the more is difference between values, the more SD. In other words SD corresponds to dispersion of data. Taking both condition, we can see that dispersion of students of A class is obviously less than that of B class. So, C

usual way:

$$SD=\sqrt{\frac{\sum{(x-x_{av})^2}}{n}}$$

1) first condition says that for class A $$|x_j-x_i|>12$$

Additionally, we can states that minimum SD is (when $$x_{av}$$ is evenly between $$x_i$$ and $$x_j$$)

$$SD_{Amin}>\sqrt{\frac{({x_j}-x_{av})^2+({x_i}-x_{av})^2}{2}}=\sqrt{\frac{6^2+6^2}{2}}=6$$

$$SD_{Amin}>6$$

2) second condition says that for class B $$|x_j-x_i|<=6$$

Additionally, we can states that maximum SD is (when $$x_{av}$$ is close to one of $$x_i$$ or $$x_j$$)

$$SD_{Bmax}<\sqrt{\frac{({x_j}-x_{av})^2+({x_i}-x_{av})^2}{2}}=\sqrt{\frac{6^2+0^2}{2}}=\frac{6}{\sqrt{2}}$$

$$SD_{Bmin}<\frac{6}{\sqrt{2}}$$

1)&2) Combine two conditions:

$$SD_{A}=>SD_{Amin}>6>\frac{6}{\sqrt{2}}>SD_{Bmin}>=SD_{B}$$

$$SD_{A}>SD_{B}$$
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Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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walker wrote:
you force me to think more carefully Walker, one more: How do you come from "statement1: the difference between the ages of any two students in class A is always more than 1 year" to :
walker wrote:
1) first condition says that for class A
, I mean |xj-xi|>12

One more: I chose E because I follow one rule from Gmatclub that if we dont know exactly specific each age, we can have no conclusion about SD!
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GMAT 1: 750 Q50 V40 Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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We have to choose the same units for age to make SD compatible. I choose months and, therefore, |xj-xi|>12

sondenso wrote:
One more: I chose E because I follow one rule from Gmatclub that if we dont know exactly specific each age, we can have no conclusion about SD!

Think about SD as an average difference between an average value and other data. The problem directly says about differences.
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GMAT 1: 750 Q50 V40 Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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snoor wrote:
My math concepts around statistics and standard deviation are weak. Can you share some resources for improvement?

I think GMAT is far far away from statistics. For many people who did not study statistics SD seems to be a mysterious feature from very difficult mathematical jungle of statistics. But GMAT does not go so deeply. Think about SD as an average deviation of data from an average value and remember the formula.
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Re: Is the standard deviation of ages of students in class A greater than  [#permalink]

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1
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: Is the standard deviation of ages of students in class A greater than  [#permalink]

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1
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: Is the standard deviation of ages of students in class A greater than  [#permalink]

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1
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: Is the standard deviation of ages of students in class A greater than  [#permalink]

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

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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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