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# Set P consists of 5 items. The standard deviation of the items in Set

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Math Expert
Joined: 02 Sep 2009
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Set P consists of 5 items. The standard deviation of the items in Set  [#permalink]

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26 Sep 2016, 03:25
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Difficulty:

75% (hard)

Question Stats:

45% (00:52) correct 55% (01:07) wrong based on 137 sessions

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Set P consists of 5 items. The standard deviation of the items in Set P is S. Is S>2?

(1) All the items in Set P are different even numbers between 1 and 19.

(2) The smallest number in the set is 10.

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Re: Set P consists of 5 items. The standard deviation of the items in Set  [#permalink]

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26 Sep 2016, 18:55
1) All the items in Set P are different even numbers between 1 and 19.
For smallest standard deviation, lets take set with numbers closest to one another.
P = {2,4,6,8,10}
mean of P = 6
Std dev = \sqrt{$$\frac{(2-6)^2+(4-6)^2 + (6-6)^2 +(8-6)^2 +(10-6)^2}{5}$$}
this is >2.
If we take any other set say P1 = {2,4,6,8,12}, P1's standard deviation will be more than that of P.

Sufficient.

(2) The smallest number in the set is 10.
P2 = {10,10,10,10,10}
Standard deviation is 0, less than 2
P3= {10,12,14,16,18}
standard deviation is same as that of P, which is greater than 2.

(2) is not sufficient

Option A.
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Re: Set P consists of 5 items. The standard deviation of the items in Set  [#permalink]

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27 Sep 2016, 06:55
Its A

Considering the lowest/ least numbers in the given range we get (2, 4, 6, 8, 10)

SD of the least set is root(8) > 2

hence for any given numbers in the range , SD is greater than 2 . Sufficient
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Set P consists of 5 items. The standard deviation of the items in Set  [#permalink]

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27 Jan 2017, 14:56
1
Bunuel wrote:
Set P consists of 5 items. The standard deviation of the items in Set P is S. Is S>2?

(1) All the items in Set P are different even numbers between 1 and 19.

(2) The smallest number in the set is 10.

Expert help please. A bit of math theory question...what is the utility of standard deviation if intuitively I think SD of set (2,4,6,8,10) should be 2? When I calculate the SD as $$\sqrt{8}$$, what is this result telling me? What would be the benefit of calculating SD with this set of numbers? I'm trying to understand the concept of SD.
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Re: Set P consists of 5 items. The standard deviation of the items in Set  [#permalink]

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28 Feb 2017, 05:19
GMAT SD problems never require to apply to SD formula itself.
Actually, SD it's the average distance between set numbers and mean.
(1) tells that the leg between numbers in sequence is 2, thus it can never be less. Suff.
(2) 10 10 10 10 10 ==> SD=0 Ans. NO
10 16 28 38 48 ==> SD>2 Ans. YES Insuff.

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Re: Set P consists of 5 items. The standard deviation of the items in Set  [#permalink]

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28 Feb 2017, 05:20
GMAT SD problems never require to apply to SD formula itself.
Actually, SD it's the average distance between set numbers and mean.
(1) tells that the leg between numbers in sequence is 2, thus it can never be less. Suff.
(2) 10 10 10 10 10 ==> SD=0 Ans. NO
10 16 28 38 48 ==> SD>2 Ans. YES Insuff.

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Re: Set P consists of 5 items. The standard deviation of the items in Set  [#permalink]

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22 Aug 2017, 00:36
raeann105 wrote:
Bunuel wrote:
Set P consists of 5 items. The standard deviation of the items in Set P is S. Is S>2?

(1) All the items in Set P are different even numbers between 1 and 19.

(2) The smallest number in the set is 10.

Expert help please. A bit of math theory question...what is the utility of standard deviation if intuitively I think SD of set (2,4,6,8,10) should be 2? When I calculate the SD as $$\sqrt{8}$$, what is this result telling me? What would be the benefit of calculating SD with this set of numbers? I'm trying to understand the concept of SD.

We dont have to calculate SD here as question is asking whether SD is greater than 2 or not. Now if we know all the values in the data set, we can find the accurate SD and can say either yes the SD is greater than 2 or no SD is not greater than 2. Thus no calculation of SD or intuition about value of SD is required in this case.
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Re: Set P consists of 5 items. The standard deviation of the items in Set &nbs [#permalink] 22 Aug 2017, 00:36
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