sd

[thephoenix]

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}

can we solve it without using formulae

[shashank.ism]

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}

can we solve it without using formulae

I think no other method is there. If anyone can throw light on this post please
calculate avg ~list of deviation~square of deviation~sum of sq deviations ~sum of sq dev/(n-1) ~ sqrt(sum of sq dev/(n-1))
0~ -3,1,2 ~ 9,1,4 ~ 14 ~ 7 ~sqrt7
0~ -2,-1,1,2 ~ 4,1,1,4 ~ 18 ~ 6 ~sqrt6
5~ -2,0,2 ~ 4,0,4 ~ 8 ~ 4 ~sqrt4
2~ -3,0,1,2 ~ 9,0,1,4 ~ 14 ~ 4.66 ~sqrt4.66
2~ -2,0,2 ~ 4,0,4 ~ 8 ~ 4 ~sqrt4

So A is the ans
any option to solve without formulae as asked by phoenix

[sars72]

i forgot the formula for SD, but was able to locate the answer by simply looking at the answer choices. SD is basically the spread of the values on either side of the mean and, on observation, it's rather obvious the the spread i.e. deviation is greatest for answer choice A

again, this is based on my relatively poor understanding of statistics. Please correct me if my reasoning is flawed.

[shashank.ism]

i forgot the formula for SD, but was able to locate the answer by simply looking at the answer choices. SD is basically the spread of the values on either side of the mean and, on observation, it's rather obvious the the spread i.e. deviation is greatest for answer choice A

again, this is based on my relatively poor understanding of statistics. Please correct me if my reasoning is flawed.

Sars u tried well and is telling a very good way of observation. But still I am not able to figure out how did u selected 1st only when we have some groups having 3 numbers and some have 4 numbers.
Will you elaborate your method so that others can get your view clearly. surely your answer is 100% correct btw.

[money9111]

i don't think the quantity of numbers influences the SD, if I'm reading into SARS' explanation correctly. you can have 100 numbers that are close together and 2 numbers that are very far apart, and the standard deviation for the 2 numbers would still be greater than that of the 100 numbers.

is this what you meant sars?

[shashank.ism]

i don't think the quantity of numbers influences the SD, if I'm reading into SARS' explanation correctly. you can have 100 numbers that are close together and 2 numbers that are very far apart, and the standard deviation for the 2 numbers would still be greater than that of the 100 numbers.

is this what you meant sars?

money1119 That is clearly evident and you can surely observe and differentiate standard deviation if they are far apart and very close.
But for this particular question its not clear. I am not asking about the definition or some explanation about SD. Bu t I wanna know from sars what how he observed and sorted out A.
would require help of any GMAT instructor

[ajith]

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}

can we solve it without using formulae

One method would be to compare the ranges and no of elements together

A) range = 5 and n =3
B) range = 4 and n =4
C) range = 4 and n =3
D) range = 5 and n =4
E) range = 4 and n =3

Look at the highest ranges and when there is tie favor the lesser n (not a scientific approach nevertheless works in this problem)

[shashank.ism]

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}

can we solve it without using formulae

One method would be to compare the ranges and no of elements together

A) range = 5 and n =3
B) range = 4 and n =4
C) range = 4 and n =3
D) range = 5 and n =4
E) range = 4 and n =3

Look at the highest ranges and when there is tie favor the lesser n (not a scientific approach nevertheless works in this problem)

Yeah that seems to be a good approach ajith..Now I can visualise what sars22 was trying to say. Yeah this could be a way to solve problem , but is that applicable to all the problems.
If we can be deadly sure that we are right in our solution in examination. After all you have to fetch marks in GMAT and you can't go on probabilities. you have to be sure you have solved problem correctly.

[Lattefah84]

I solved this using the formula for SD but it took very long time. So, is this thing with range applicable to all the problems or we have to search for some way that is sure?

[shashank.ism]

I solved this using the formula for SD but it took very long time. So, is this thing with range applicable to all the problems or we have to search for some way that is sure?

Now I understood the thing. yeah this kind of approach of range can be clearly applied to all the problems, until we get some confusing case and a combination of large numbers.

[amittilak]

My approach was slightly similar to one used by another poster here. However, instead of Range, calculated the mean for all the choices and found the sets with the farthest spread from the mean. Answer choice A and D have same maximum spread from the mean. However, since Answer choice D has more number of variables than Answer choice A, I will go with A. This is the quickest method I can think of under 2 minutes. Maybe, if I am ahead of time during my GMAT, I might consider calculating SD quickly for choices A and D.

[Ian Stewart]

First, I'm not sure I've ever seen a GMAT question which requires you to compare the standard deviations of sets which are of different sizes. In general, it isn't easy to do quickly and reliably. The method ajith suggests will work most of the time for very small sets, but certainly won't work all the time (as he acknowledged). If you take, for example, the following two sets:

A = {0, 6}
B = {0, 50, 50, 50, 50, 50, ...., 50, 50, 50, 50, 50, 100}

where B contains, say, one million elements equal to 50, then the range of B is much greater than the range of A, but because so many elements in B are equal to the mean, the standard deviation of B is almost zero, and is smaller than the standard deviation of A. That's a long way of saying that sometimes a set can have a larger range but a smaller standard deviation than another set.

[komal]

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}

can we solve it without using formulae

Look for range and # of elements in the set.

A set with higher the range and fewer the number of element has the higher SD. i.e. A

[kstv]

SD = √Σ(x-Mean)^2 /No of element

So range and no of elements determines the value of SD

[Ian Stewart]

Look for range and # of elements in the set.

A set with higher the range and fewer the number of element has the higher SD. i.e. A

I'd just like to emphasize that this is not true in general, even if it may give you the correct answer when dealing with very small sets. If you see a DS question like the following:

Is the standard deviation of data set S greater than the standard deviation of data set T?

1. The range of S is greater than the range of T.

2. S contains ten elements, and T contains eleven elements.



then even though S has fewer elements *and* a greater range than T, we still cannot say if it has a higher standard deviation; the answer is E. It might be, for example, that

S = {0, 5, 5, 5, 5, 5, 5, 5, 5, 10}
and
T = {1, 1, 1, 1, 1, 5, 9, 9, 9, 9, 9}

and T has a standard deviation considerably larger than S.