Hi Friends,
My answer and OA were different. Could somebody please validate my result. Detailed OE was not there.
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
My approach:
A and B alone are not sufficient since they give information about only 1 class. We could have various combinations for the other class.
Lets take the statements together.
For class A "always more than 1 year", hence we could determine the MINIMUM standard deviation
Mean is 15. If we plug the following values we will get the MINIMUM standard deviation
12.5 13.5 14.5 15.5 16.5 17.5.
This is closest that we can keep the values and meet the conditions. Minimum Standard deviation = 2.5. However, the standard deviation can be more also.
For class B "No student.... more than 6 month older", hence we could determine the MAXIMUM standard deviation
Mean is 16. If we plug the following values we will get the MAXIMUM standard deviation
13.25 13.75 14.25 14.75 15.25 15.75 16.25 16.75 17.25 17.75 18.25 18.75
This is the farthest we can keep the values and meet the conditions.
hence MAXIMUM standard deviation = 2.75
At this point we can see that the standard deviation of B is more than A, however we determined the Minimum standard deviation for A and maximum for B. So the value for A can also be more than B.
We do not know for sure that the standard deviation for A is more than A since by plugging values we got it less as well.
My answer E, OA is C
OE: In combination: the statements are sufficient since (1) gives info about the standard deviation of A and (2) for B. Although you cannot determine the exact standard deviations of either class, you can see that class B has a much narrower distribution of members than class A and from this you could determine that class A would have a greater standard deviation than class B . Choice C is the correct answer.
My answer and OA were different. Could somebody please validate my result. Detailed OE was not there.
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
My approach:
A and B alone are not sufficient since they give information about only 1 class. We could have various combinations for the other class.
Lets take the statements together.
For class A "always more than 1 year", hence we could determine the MINIMUM standard deviation
Mean is 15. If we plug the following values we will get the MINIMUM standard deviation
12.5 13.5 14.5 15.5 16.5 17.5.
This is closest that we can keep the values and meet the conditions. Minimum Standard deviation = 2.5. However, the standard deviation can be more also.
For class B "No student.... more than 6 month older", hence we could determine the MAXIMUM standard deviation
Mean is 16. If we plug the following values we will get the MAXIMUM standard deviation
13.25 13.75 14.25 14.75 15.25 15.75 16.25 16.75 17.25 17.75 18.25 18.75
This is the farthest we can keep the values and meet the conditions.
hence MAXIMUM standard deviation = 2.75
At this point we can see that the standard deviation of B is more than A, however we determined the Minimum standard deviation for A and maximum for B. So the value for A can also be more than B.
We do not know for sure that the standard deviation for A is more than A since by plugging values we got it less as well.
My answer E, OA is C
OE: In combination: the statements are sufficient since (1) gives info about the standard deviation of A and (2) for B. Although you cannot determine the exact standard deviations of either class, you can see that class B has a much narrower distribution of members than class A and from this you could determine that class A would have a greater standard deviation than class B . Choice C is the correct answer.
