Standard Deviation

[maria]

which of the following distribution of numbers has the greatest standard deviation?
A. {-3, 1, 2}
B. {-2, -1, 1, 2}
C. {3, 5, 7}
D. {-1, 2, 3, 4}
E. {0, 2, 4}

Pls show me some strategies to do standard deviation since I am usually scared of it. Thanks

[aatech]

For this you have to see which set is widely spread.. this is what SD is all about...

If nos are not ordered, put them in increasing order and calculate the approx mean.. then compare the extreme nos of each set with the mean and check which one is widely spread...

Here ANS should be A

OA???

[jaganbravo]

which of the following distribution of numbers has the greatest standard deviation?
A. {-3, 1, 2} mean =0
B. {-2, -1, 1, 2} mean=0
C. {3, 5, 7}mean=5
D. {-1, 2, 3, 4}mean=4
E. {0, 2, 4} mean=2

Answer should be D.

[maria]

@ Aatech, your answer is right, I think. But in order to get the answer, it takes me long with some steps to get the SD value of each set. I wonder I have enough time to do it in the actual test. Do you have a shorter way to get the answer? Thank you.

@ Jaganbravo, why is the answer D while its value of mean is not the biggest? can you give a clearer explanation? Thanks

[netigen]

which of the following distribution of numbers has the greatest standard deviation?
A. {-3, 1, 2} mean =0 ---> 14/3
B. {-2, -1, 1, 2} mean=0 --> 10/4
C. {3, 5, 7}mean=5 ---> 8/3
D. {-1, 2, 3, 4}mean=2 ---> 14/4
E. {0, 2, 4} mean=2 ---> 8/3

so ans is A

Note: C and E have the same distribution so only need to calculate SD^2 for one

[aatech]

maria,

I didn't calculate anything.. Numbers are already ordered in the question so you don't need to do that part.. Moreover, the nos are really small so that one can get the approx mean w/o pen and paper...

Once you have the approx mean of each set, you are just comparing the extreme nos to check which one is widely spread..

PS: THERE IS NO NEED TO CALCULATE SD

Hope this helps
aatech

[AleksandrM]

I, too, think the answer should be D. What is the OA??

[maria]

Hello AleksandrM,
It is A.
In order to know which set has the greatest standard deviation, we must find out the standard deviation of each set as Netigen did.

A. {-3, 1, 2} mean =0 ---> 14/3
B. {-2, -1, 1, 2} mean=0 --> 10/4
C. {3, 5, 7}mean=5 ---> 8/3
D. {-1, 2, 3, 4}mean=2 ---> 14/4
E. {0, 2, 4} mean=2 ---> 8/3

Or we will "....calculate the approx mean.. then compare the extreme nos of each set with the mean and check which one is widely spread.." The greater the data are spread away from the mean, the greater the standard deviation.

Why do you think it is D?

[/quote]

[AleksandrM]

I just looked at the general spread between the numbers. Obviously my approach is too simplistic for a problem of this difficulty. I know how to calculate the SD. However, most of the books I studies from said that I will not be asked to solve the SD on the test, so I assumed that these tests are correct.

[Mclaughlin]

which of the following distribution of numbers has the greatest standard deviation?
A. {-3, 1, 2} mean =0 ---> 14/3
B. {-2, -1, 1, 2} mean=0 --> 10/4
C. {3, 5, 7}mean=5 ---> 8/3
D. {-1, 2, 3, 4}mean=2 ---> 14/4
E. {0, 2, 4} mean=2 ---> 8/3

so ans is A

Note: C and E have the same distribution so only need to calculate SD^2 for one

I'm sorry i'm not good at SD so i was wondering if you could explain how you got the number 14 in answer A, 10 in b, etc. I obviously know how you got the second number.