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Math Expert V
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What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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Question Stats: 59% (01:24) correct 41% (01:26) wrong based on 173 sessions

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What is the standard deviation of a set of numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal

(2) The sum of the squares of the differences from the mean is greater than 100

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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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SD is sum of squares of each term from the mean,

Statement 1 states, Value of difference with each term is constant. Thus the statement can be reduces to all the terms in the list are equal. Hence the SD = 0

I choose A

Though i am not sure whether i understood the STatement 1 properly. Please correct me if i am wrong
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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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It's absolute value which is same
Like -5&+5 have same absolute value of difference from 0

Sent from my XT1033 using GMAT Club Forum mobile app
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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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Nikki&amp;sunny wrote:
It's absolute value which is same
Like -5&+5 have same absolute value of difference from 0

Sent from my XT1033 using GMAT Club Forum mobile app

As per your point,

then set may contain either positive or negative numbers, by which we can't determine the SD
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What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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3
deepthit

Statement (1) does not give us any information about the value of Standard Deviation.

Check out these cases : 1) 19,20,21. Mean=20. The absolute value of (19-20) and (21-20) is the same. Standard deviation=1.
2) 18,20,24. Mean=20. The absolute value of (18-20) and (22-20) is the same. Standard deviation=2.

Therefore, we can't find the exact value of SD.

Statement (2) Σ(xi-median)>100. Xis could taky any value. Not sufficient.

(1) + (2) Again Xs could take a lot of values and still be >100.

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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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1
InAthens wrote:
deepthit

Statement (1) does not give us any information about the value of Standard Deviation.

Check out these cases : 1) 19,20,21. Mean=20. The absolute value of (19-20) and (21-20) is the same. Standard deviation=1.
2) 18,20,24. Mean=20. The absolute value of (18-20) and (22-20) is the same. Standard deviation=2.

Therefore, we can't find the exact value of SD.

Note that there is a problem with these cases. Not that it changes the answer, though.

" The absolute value of the difference of each number in the set from the mean is equal"

So the cases should be
1) 19, 21 (when you add 20 to the mix, its difference from mean is 0, not 1)
2) 18, 22
3) 18, 18, 22, 22
etc
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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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VeritasPrepKarishma wrote:
InAthens wrote:
deepthit

Statement (1) does not give us any information about the value of Standard Deviation.

Check out these cases : 1) 19,20,21. Mean=20. The absolute value of (19-20) and (21-20) is the same. Standard deviation=1.
2) 18,20,24. Mean=20. The absolute value of (18-20) and (22-20) is the same. Standard deviation=2.

Therefore, we can't find the exact value of SD.

Note that there is a problem with these cases. Not that it changes the answer, though.

" The absolute value of the difference of each number in the set from the mean is equal"

So the cases should be
1) 19, 21 (when you add 20 to the mix, its difference from mean is 0, not 1)
2) 18, 22
3) 18, 18, 22, 22
etc

Hi Karishma,
for this question correct answer is E , however if we were given that there are 3 numbers in the set , i think even then answer would have been E? Because the numbers could be anything? Am I correct?

Thanks
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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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1
rakaisraka wrote:
VeritasPrepKarishma wrote:
InAthens wrote:
deepthit

Statement (1) does not give us any information about the value of Standard Deviation.

Check out these cases : 1) 19,20,21. Mean=20. The absolute value of (19-20) and (21-20) is the same. Standard deviation=1.
2) 18,20,24. Mean=20. The absolute value of (18-20) and (22-20) is the same. Standard deviation=2.

Therefore, we can't find the exact value of SD.

Note that there is a problem with these cases. Not that it changes the answer, though.

" The absolute value of the difference of each number in the set from the mean is equal"

So the cases should be
1) 19, 21 (when you add 20 to the mix, its difference from mean is 0, not 1)
2) 18, 22
3) 18, 18, 22, 22
etc

Hi Karishma,
for this question correct answer is E , however if we were given that there are 3 numbers in the set , i think even then answer would have been E? Because the numbers could be anything? Am I correct?

Thanks

If there are 3 numbers in the set such that mean = 20 and "the absolute value of the difference of each number in the set from the mean is equal", then the SD will be 0.
Say, the absolute value of the difference of each number from the mean is 0. Then all numbers are the same and equal to 20. SD = 0
Say, the absolute value of the difference of each number from the mean is 1. So the difference of each number from mean is either +1 or -1. If you have an odd number of numbers (i.e. 3), the shortfall deviation and excess deviation will not be equal. That is, you will have either 19, 19, 21 or 19, 21, 21. The mean here will not be 20.
Same will be true for any absolute value of difference from mean which is other than 0.
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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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Hello Karishma,

Dont get your explanation. In the question above, even if there are 3 numbers the answer would be E, right Ex {1,2,3} SD <> 0. Unless we know the exact element values in set we cant tell the SD. Correct me if otherwise ?
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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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coolkl wrote:
Hello Karishma,

Dont get your explanation. In the question above, even if there are 3 numbers the answer would be E, right Ex {1,2,3} SD <> 0. Unless we know the exact element values in set we cant tell the SD. Correct me if otherwise ?

Look at your example: {1, 2,3}

Is "the absolute value of the difference of each number in the set from the mean is equal"?

Mean is 2.
Absolute value of diff between 1 and 2 is 1.
Absolute value of diff between 3 and 2 is 1.
But Absolute value of diff between 2 and 2 is 0.

Now go back to the logic I have explained above.
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Re: What is the standard deviation of a set of numbers whose mean is 20?  [#permalink]

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If there are 3 numbers in the set such that mean = 20 and "the absolute value of the difference of each number in the set from the mean is equal", then the SD will be 0.
Say, the absolute value of the difference of each number from the mean is 0. Then all numbers are the same and equal to 20. SD = 0
Say, the absolute value of the difference of each number from the mean is 1. So the difference of each number from mean is either +1 or -1. If you have an odd number of numbers (i.e. 3), the shortfall deviation and excess deviation will not be equal. That is, you will have either 19, 19, 21 or 19, 21, 21. The mean here will not be 20.
Same will be true for any absolute value of difference from mean which is other than 0.

Hi karishma

Following is what I get from your explanation.

When we are provided 2 info below.
+ value of mean, and
+ "the absolute value of the difference of each number in the set from the mean is equal"

Then we can conclude that
- If the set contains an odd number of numbers (i.e. 3, 5, 7, etc.) --> S.D = 0
- If the set contains an even number of numbers (i.e. 2, 4, 6, etc.) --> S.D can't be determined.

Am I right?
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