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Standard deviation

by Ramit88 » Thu Jan 20, 2011 2:22 am
If sets A & B have the same number of terms, is the Standard deviation of set A greater than the Standard deviation of set B ?

1. the range of set A is greater than the range of B
2. sets A & B are both evenly spaced sets

[spoiler]ANS:C[/spoiler]

but i read somewhere if sets have same no. of digits then the set with higher range have greater Standard deviation .. can someone please explain this to me
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by btgyes » Thu Jan 20, 2011 6:34 am
IMO A
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by jaxis » Thu Jan 20, 2011 7:13 am
ramit,

Consider this example:
A={-3,0,0,0,0,0,3}
Number of terms =7
range = 6
mean =0
sd = sqrt(18/7)

B={-2,-2,-2,0,2,2,2}
Number of terms =7
range = 4
mean =0
sd = sqrt(24/7)

N(A) = N(B)
Range(A)>Range(B)
SD(A) < SD(B)
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by btgyes » Thu Jan 20, 2011 11:43 pm
jaxis wrote:ramit,

Consider this example:
A={-3,0,0,0,0,0,3}
Number of terms =7
range = 6
mean =0
sd = sqrt(18/7)

B={-2,-2,-2,0,2,2,2}
Number of terms =7
range = 4
mean =0
sd = sqrt(24/7)

N(A) = N(B)
Range(A)>Range(B)
SD(A) < SD(B)

BUT

if you take B = {-2,0,0,0,0,0,2}

Then SD = sqrt(8/7)

and SD(A) > SD (B)

So i think we need to consider 2nd Statement as well which says that

both sets are evenly spaced sets.

what i interpret from this statement is that difference b/w two consecutive items in both sets should be same.

eg.

Set A = ( -5 , -3, -1 , 1, 3) # difference of 2 b/w consecutive items

=> SD = sqrt(10)

and

Set B = ( -4 , -2 , 0 , 2, 4) # difference of 2 b/w consecutive items

=> SD = sqrt(8)

SD (A) > SD (B)

Hence Ans is C
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by GMATGuruNY » Fri Jan 21, 2011 6:22 am
Ramit88 wrote:If sets A & B have the same number of terms, is the Standard deviation of set A greater than the Standard deviation of set B ?

1. the range of set A is greater than the range of B
2. sets A & B are both evenly spaced sets

[spoiler]ANS:C[/spoiler]

but i read somewhere if sets have same no. of digits then the set with higher range have greater Standard deviation .. can someone please explain this to me
Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:

Do the values in set A deviate more from the mean than the do values in set B?

Let SD = standard deviation.

Statement 1:
We know that the distance between the biggest and smallest values in A is greater than the distance between the biggest and smallest values in B.
But we don't know the mean, and to determine which set has a greater SD, we need to know how all the numbers in each set -- not just the biggest and smallest -- are deviating from the mean.
Insufficient.

Statement 2:
When values are evenly spaced, the mean = the median, and all the values are symmetrical about the median.
For example, if m = median, and all the values are consecutive even or odd integers, the set will look like this:

...m-6, m-4, m-2, m, m+2, m+4, m+6...

But to determine which set has a greater SD, we need to know in each set the distance between each successive pair of values. For example:

If A = consecutive even integers = {2,4,6} and B = consecutive multiples of 3 = {3,6,9}, then the values in B deviate more from the mean and B has the larger SD.
If A = consecutive multiples of 3 = {3,6,9} and B = consecutive even integers = {2,4,6}, then the values in A deviate more from the mean and A has the larger SD.
Insufficient.

Statements 1 and 2:
A and B have the same number of values.
A and B are both evenly spaced sets, so the values in each set are symmetrical about the mean.
The range in A is greater.
For A to have a greater range, the distance between each successive pair in A must be greater than the distance between each successive pair in B. In other words, the values in A are more spread out.
Thus, the values in A are deviating more from the mean, and A has a larger SD.
Sufficient.

The correct answer is C.
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by chendawg » Thu Feb 10, 2011 11:10 am
^^^^

Great explanation!

What's the source of this problem?
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by giovanni.gastone » Sat May 28, 2011 10:24 pm
GMATGuruNY wrote:
Ramit88 wrote:If sets A & B have the same number of terms, is the Standard deviation of set A greater than the Standard deviation of set B ?

1. the range of set A is greater than the range of B
2. sets A & B are both evenly spaced sets

[spoiler]ANS:C[/spoiler]

but i read somewhere if sets have same no. of digits then the set with higher range have greater Standard deviation .. can someone please explain this to me
Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:

Do the values in set A deviate more from the mean than the do values in set B?

Let SD = standard deviation.

Statement 1:
We know that the distance between the biggest and smallest values in A is greater than the distance between the biggest and smallest values in B.
But we don't know the mean, and to determine which set has a greater SD, we need to know how all the numbers in each set -- not just the biggest and smallest -- are deviating from the mean.
Insufficient.

Statement 2:
When values are evenly spaced, the mean = the median, and all the values are symmetrical about the median.
For example, if m = median, and all the values are consecutive even or odd integers, the set will look like this:

...m-6, m-4, m-2, m, m+2, m+4, m+6...

But to determine which set has a greater SD, we need to know in each set the distance between each successive pair of values. For example:

If A = consecutive even integers = {2,4,6} and B = consecutive multiples of 3 = {3,6,9}, then the values in B deviate more from the mean and B has the larger SD.
If A = consecutive multiples of 3 = {3,6,9} and B = consecutive even integers = {2,4,6}, then the values in A deviate more from the mean and A has the larger SD.
Insufficient.

Statements 1 and 2:
A and B have the same number of values.
A and B are both evenly spaced sets, so the values in each set are symmetrical about the mean.
The range in A is greater.
For A to have a greater range, the distance between each successive pair in A must be greater than the distance between each successive pair in B. In other words, the values in A are more spread out.
Thus, the values in A are deviating more from the mean, and A has a larger SD.
Sufficient.

The correct answer is C.
Really good explanation. Thank you.
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by ronnie1985 » Wed Apr 04, 2012 9:21 am
S1: Std deviation is not a function of range unless it is a normal distribution which is not specifically told in the statement

S2: At least one term of each element is required

Comb: Can easily say which set has higher std deviation

(C) is ans
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by anujan007 » Sat Jul 21, 2012 4:46 pm
I worked on it the way Mitch has mentioned and came down to the choice of whether the answer was C or E.

I concluded that since there is no way to know the mean with both statements, both together are insufficient and hence chose E.

After going through the explanation, realized my mistake. This will surely help should I face such a problem again.

Thanks Mitch!
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by zazoz » Mon Sep 10, 2012 3:05 am
IMO C, @ 10 sec
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by zazoz » Mon Sep 10, 2012 3:05 am
IMO C, @ 10 sec
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by eski » Tue Sep 18, 2012 11:48 am
I have a question, my take home is

to get SD only 2 parameters imp?
1. mean
2. spread that can be range , indivual values, etc

am i correct?
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by rajeshsinghgmat » Sun Apr 21, 2013 5:08 am
D

when the number of terms are same the set with greater range has greater deviation.

for sets with even spaced elements the deviation is same.
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by MartyMurray » Sun Nov 23, 2014 6:18 am
rajeshsinghgmat wrote:D

when the number of terms are same the set with greater range has greater deviation.

for sets with even spaced elements the deviation is same.
Rajesh,

To get this right, you need to look at it a little more closely.

Standard deviation is about all the elements in a set. Range is only about the biggest and smallest element in a set. For instance, a set with a wide range could have a tight, mean centered cluster of most elements. So the range of that set could be greater than that of another set without the standard deviation of the first being greater than that of that other set.

Regarding the spacing of the elements, the elements are evenly spaced within each set. This does not mean that the spacing in one set is the same as the spacing in the other set. So there is no way to tell from this if the standard deviations are the same.
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by nikhilgmat31 » Wed Sep 02, 2015 5:30 am
GMATGuruNY wrote:
Ramit88 wrote:If sets A & B have the same number of terms, is the Standard deviation of set A greater than the Standard deviation of set B ?

1. the range of set A is greater than the range of B
2. sets A & B are both evenly spaced sets

[spoiler]ANS:C[/spoiler]

but i read somewhere if sets have same no. of digits then the set with higher range have greater Standard deviation .. can someone please explain this to me
Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased:

Do the values in set A deviate more from the mean than the do values in set B?

Let SD = standard deviation.

Statement 1:
We know that the distance between the biggest and smallest values in A is greater than the distance between the biggest and smallest values in B.
But we don't know the mean, and to determine which set has a greater SD, we need to know how all the numbers in each set -- not just the biggest and smallest -- are deviating from the mean.
Insufficient.

Statement 2:
When values are evenly spaced, the mean = the median, and all the values are symmetrical about the median.
For example, if m = median, and all the values are consecutive even or odd integers, the set will look like this:

...m-6, m-4, m-2, m, m+2, m+4, m+6...

But to determine which set has a greater SD, we need to know in each set the distance between each successive pair of values. For example:

If A = consecutive even integers = {2,4,6} and B = consecutive multiples of 3 = {3,6,9}, then the values in B deviate more from the mean and B has the larger SD.
If A = consecutive multiples of 3 = {3,6,9} and B = consecutive even integers = {2,4,6}, then the values in A deviate more from the mean and A has the larger SD.
Insufficient.

Statements 1 and 2:
A and B have the same number of values.
A and B are both evenly spaced sets, so the values in each set are symmetrical about the mean.
The range in A is greater.
For A to have a greater range, the distance between each successive pair in A must be greater than the distance between each successive pair in B. In other words, the values in A are more spread out.
Thus, the values in A are deviating more from the mean, and A has a larger SD.
Sufficient.

The correct answer is C.

Hi Mitch,

Can you please explain statement 1 by picking some numbers. I am not able to visualize any numbers to prove statement 1 is not sufficient.
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