stats ques

[nitug]

hi ppl,

please go through this one and see if anyone can explain me the answer.

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?
1. All elements of set T are positive
2. The range of set T is 0
• Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
• Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
• EACH statement ALONE is sufficient
• Statements (1) and (2) TOGETHER are NOT sufficient


ans is B.

thanks,
Nitug

[parallel_chase]

hi ppl,

please go through this one and see if anyone can explain me the answer.

Set T consists of a certain number of even integers divisible by 3. Is standard deviation of T positive?
1. All elements of set T are positive
2. The range of set T is 0
• Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
• Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
• EACH statement ALONE is sufficient
• Statements (1) and (2) TOGETHER are NOT sufficient


ans is B.

thanks,
Nitug

From next time kindly use spoiler tag for the answer.

The set consists of even multiples of 3.

Statement I

All elements of set T are positive

We dont know what is the median, what is the mean, or even the number of elements in the set. Hence we cannot even find the SD.
Therefore Insufficient.

Statement II

The range of the set is 0

We also know that the set consists of even multiples of 3.

6,6,6,6,6

mean is 6
range is 0
SD = 0

-12,-12,-12
mean is -12
range is 0
SD = 0

Therefore for any number of the set positive or negative, the SD is 0.

0 is neither positive nor negative.

Hence the SD is not positive, statement is sufficient.

Hence B is the answer.

Hope this helps.

[nitug]

thanks a lot parallel_chase!!
this explained the ques very well...

and aplogies for giving the answer....


will keep that in mind next time!!

[gmattestprep]

Standard deviation is always positive based on how its calculated. How come these choices then?

[Ian Stewart]

Standard deviation is always positive based on how its calculated. How come these choices then?

That's not quite true. What is true is that the standard deviation cannot be negative. It can be zero, however, and in one case only: when all the elements in a set are the same. The set {7, 7, 7, 7}, for example, has a standard deviation of zero.

[ashish2104]

I have one question here.

If set T = {-12,6,12}, range is 0
mean = 2
SD is positive

I don't understand why do we select only same integers for set T.

[Ian Stewart]

I have one question here.

If set T = {-12,6,12}, range is 0
mean = 2
SD is positive

I don't understand why do we select only same integers for set T.

The range of a set is equal to the difference between the largest and smallest elements. In the example set you give, {-12,6,12}, the range is 12 - (-12) = 24.

The range of a set can only be zero if all the elements in the set are equal.