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Is the standard deviation of set A is greater than standard deviation

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Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post 06 Jul 2020, 23:55
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A
B
C
D
E

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Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post Updated on: 08 Jul 2020, 04:51
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Is the standard deviation of set A is greater than standard deviation of set B ?

Thinking this way, it becomes easy to answer this questions.
As questions asks to find which SD is greater then first thing that must pop is that there must be relationship between the two sets - A and B.
So...

(1) Set A consists of consecutive multiples of 10
Clearly, not sufficient.

(2) Set B consists of consecutive multiples of 2
Clearly, not sufficient.

Hence answer must be either C or E. Here, it looks like details of two sets are available and we might be tempted to pick C which is a trap. Here's why

Together 1 and 2.
\(SD(σ) = \sqrt{variance} = \sqrt{\frac{∑(x_i - x_{avg})^2}{n}}\)

As you can see SD depends on three parameters. So, \(SD_A < SD_B\) or \(SD_A > SD_B\) because it depends on 'n - number of elements in the set'. For example
Let Set A = {10, 20, 30}, \(SD_A = \frac{2*10^2}{3}\)
Set B = {2, 4, 6}, \(SD_B = \frac{2*2^2}{3}\)
Then \(SD_A > SD_B\)

But if
Set A = {10, 20, 30}, \(SD_A = \frac{2*10^2}{3}\)
Set B = {2, 4, 6, 8, .... , 98}, \(SD_B = \frac{2(48^2 + 46^2 + ... + 2)}{49}\)
Then \(SD_A < SD_B\)

Answer E.
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Originally posted by unraveled on 07 Jul 2020, 00:30.
Last edited by unraveled on 08 Jul 2020, 04:51, edited 3 times in total.
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Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post Updated on: 08 Jul 2020, 00:34
IMO E

(1) Set A consists of consecutive multiples of 10

No information about Set B.
Not Sufficient


(2) Set B consists of consecutive multiples of 2

No information about Set A.
Not Sufficient


Together:
Standard deviation depends on number of terms.
Since we have no idea about number of terms in both set.
So Not Sufficient.

Originally posted by MayankSingh on 07 Jul 2020, 00:32.
Last edited by MayankSingh on 08 Jul 2020, 00:34, edited 1 time in total.
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Re: Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post 07 Jul 2020, 04:32
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Note: Range Rule of Determining SD states that the SD of a set is equal to 1/4 of its range.

(1) Set A consists of consecutive multiples of 10
No information about set B.
(Insufficient)

(2) Set B consists of consecutive multiples of 2
No information about set A.
(Insufficient)

Statement 1&2 together:

Case 1:
Let Set A = {10,20,30,40}
Set B = {10,20,30,40}
S.D. will be equal.

Case 2: SET A = {10,20,30,40}
Range = 40-10 = 30
SD = 30/4 = 7.5

Set B = {2,8,14,20,26,32,38}
Range = 38-2 = 36
SD = 36/4 = 9

SD of Set B is greater

Case 3: SET A = {10,20,30,40}
Range = 40-10 = 30
SD = 30/4 = 7.5

Set B = {2,8,14,20}
Range = 20-2 = 18
SD = 18/4 = 4.5

SD of Set A is greater

(Insufficient)

IMO E

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Re: Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post 07 Jul 2020, 04:41
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In theory, the standard deviation of either set could be zero if one of the sets contains only one element. If we allow that possibility, the answer is immediately E.

If we disallow that possibility, then if the set of consecutive multiples of 10 is {10, 20}, its standard deviation is 5 (every element in the set is 5 away from the mean, so that is automatically the standard deviation). If you take a very large set of consecutive multiples of 2, say all the multiples of 2 between 0 and 1000, almost every value in this set will be more than 5 away from the mean, and the standard deviation will be much larger than 5. So the answer is still E.

If we knew the sets were the same size, then both statements would be sufficient together, since then the elements of A would be a greater distance apart than the elements of B (in fact, the standard deviation of A would be precisely five times as big as that of B, because the distances within A would be five times as big).
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Re: Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post 07 Jul 2020, 21:20
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Ans - E

Standard deviations is under root of variance, which is diff of term and the av, the more this deviation is the more is SD

Statement 1
Given info on set A, but no B. Not sufficient

Statement B
Gives info on set B, but no A, Not sufficient

With Statement 1 and 2
Even if Set A is consecutive multiple of 10, and set B is consecutive multiple of 2.

It is unsure what would the variance be depending of the starting number. Set B can still be a multiple of set A, which will prove otherwise.

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Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post 08 Jul 2020, 00:03
Standard deviation depends on the variance and also number of terms in the set.Here in both the statements we don't have number of terms mentioned so we can't conclude from any of the statements.

Answer E
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Re: Is the standard deviation of set A is greater than standard deviation  [#permalink]

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New post 04 Aug 2020, 20:40
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Re: Is the standard deviation of set A is greater than standard deviation   [#permalink] 04 Aug 2020, 20:40

Is the standard deviation of set A is greater than standard deviation

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