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To find the same standard deviation

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by gmattesttaker2 » Sat Jan 11, 2014 6:39 pm
Hello,

Can you please assist with this:

Which of the following sets has the same standard deviation as set {m, n, p, q, r}?

A) {m/2,n/2,p/2,q/2,r/2}
B) { m^2, n^2, p^2, q^2, r^2 }
C) {m + 2, n + 2, p + 2, q + 2, r + 2}
D) {2m,2n,2p,2q,2r}
E) {|m|,|n|,|p|,|q|,|r|}

OA: C


I was wondering when will E be wrong since absolute value will always be positive.

Thanks a lot.

Best Regards,
Sri
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by Uva@90 » Sat Jan 11, 2014 7:17 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

Which of the following sets has the same standard deviation as set {m, n, p, q, r}?

A) {m/2,n/2,p/2,q/2,r/2}
B) { m^2, n^2, p^2, q^2, r^2 }
C) {m + 2, n + 2, p + 2, q + 2, r + 2}
D) {2m,2n,2p,2q,2r}
E) {|m|,|n|,|p|,|q|,|r|}

OA: C


I was wondering when will E be wrong since absolute value will always be positive.

Thanks a lot.

Best Regards,
Sri
Hi Sri,
The Concept behind this question is,
If we add or subtract a constant to each term in a set Mean will increase or decrease by the same constant SD will not change.

Considering the above statement Answer will be C

Coming to you question
Why Not E?
E option will always be Positive, but set {m, n, p, q, r} may have negative values, as
Let set {2,-2,-1,1} wil not have same SD as {2,2,1,1}

Hope I made it clear.

Earlier even I had same confusion. Later Brent and Mitch had explained me clearly.
Here is the link for the same,
https://www.beatthegmat.com/standard-dev ... tml#701110

Regards,
Uva
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by Brent@GMATPrepNow » Sat Jan 11, 2014 9:39 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

Which of the following sets has the same standard deviation as set {m, n, p, q, r}?

A) {m/2,n/2,p/2,q/2,r/2}
B) { m^2, n^2, p^2, q^2, r^2 }
C) {m + 2, n + 2, p + 2, q + 2, r + 2}
D) {2m,2n,2p,2q,2r}
E) {|m|,|n|,|p|,|q|,|r|}

OA: C


I was wondering when will E be wrong since absolute value will always be positive.

Thanks a lot.

Best Regards,
Sri
Here's another example to show why the correct answer is not E.

If the set is {-1, -1, 1, 1} the Standard Deviation is definitely NOT zero (since the standard deviation is only zero when all of the elements in the set are equal)

For answer choice E, we find the absolute value of each element in the set. When we do so, we get {1, 1, 1, 1}, and the Standard Deviation is definitely zero

Cheers,
Brent
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by gmattesttaker2 » Tue Jan 14, 2014 10:01 pm
Uva@90 wrote:
gmattesttaker2 wrote:Hello,

Can you please assist with this:

Which of the following sets has the same standard deviation as set {m, n, p, q, r}?

A) {m/2,n/2,p/2,q/2,r/2}
B) { m^2, n^2, p^2, q^2, r^2 }
C) {m + 2, n + 2, p + 2, q + 2, r + 2}
D) {2m,2n,2p,2q,2r}
E) {|m|,|n|,|p|,|q|,|r|}

OA: C


I was wondering when will E be wrong since absolute value will always be positive.

Thanks a lot.

Best Regards,
Sri
Hi Sri,
The Concept behind this question is,
If we add or subtract a constant to each term in a set Mean will increase or decrease by the same constant SD will not change.

Considering the above statement Answer will be C

Coming to you question
Why Not E?
E option will always be Positive, but set {m, n, p, q, r} may have negative values, as
Let set {2,-2,-1,1} wil not have same SD as {2,2,1,1}

Hope I made it clear.

Earlier even I had same confusion. Later Brent and Mitch had explained me clearly.
Here is the link for the same,
https://www.beatthegmat.com/standard-dev ... tml#701110

Regards,
Uva
Hello Uva,

Thank you very much for the explanation and for sharing the link.

Best Regards,
Sri
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by gmattesttaker2 » Tue Jan 14, 2014 10:01 pm
Uva@90 wrote:
gmattesttaker2 wrote:Hello,

Can you please assist with this:

Which of the following sets has the same standard deviation as set {m, n, p, q, r}?

A) {m/2,n/2,p/2,q/2,r/2}
B) { m^2, n^2, p^2, q^2, r^2 }
C) {m + 2, n + 2, p + 2, q + 2, r + 2}
D) {2m,2n,2p,2q,2r}
E) {|m|,|n|,|p|,|q|,|r|}

OA: C


I was wondering when will E be wrong since absolute value will always be positive.

Thanks a lot.

Best Regards,
Sri
Hi Sri,
The Concept behind this question is,
If we add or subtract a constant to each term in a set Mean will increase or decrease by the same constant SD will not change.

Considering the above statement Answer will be C

Coming to you question
Why Not E?
E option will always be Positive, but set {m, n, p, q, r} may have negative values, as
Let set {2,-2,-1,1} wil not have same SD as {2,2,1,1}

Hope I made it clear.

Earlier even I had same confusion. Later Brent and Mitch had explained me clearly.
Here is the link for the same,
https://www.beatthegmat.com/standard-dev ... tml#701110

Regards,
Uva
Hello Uva,

Thank you very much for the explanation and for sharing the link.

Best Regards,
Sri
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