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# Set V consists of 2 distinct positive values. What is the standard dev

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Math Expert
Joined: 02 Sep 2009
Posts: 60460
Set V consists of 2 distinct positive values. What is the standard dev  [#permalink]

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01 Nov 2019, 07:53
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55% (hard)

Question Stats:

53% (01:15) correct 47% (01:19) wrong based on 58 sessions

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Set V consists of 2 distinct positive values. What is the standard deviation of set V?

(1) The mean of the set is 10.
(2) The range of the set is 10.

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Joined: 20 Jul 2017
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Location: India
Concentration: Entrepreneurship, Marketing
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Re: Set V consists of 2 distinct positive values. What is the standard dev  [#permalink]

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01 Nov 2019, 08:17
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Bunuel wrote:
Set V consists of 2 distinct positive values. What is the standard deviation of set V?

(1) The mean of the set is 10.
(2) The range of the set is 10.

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Let the 2 distinct values of the set = {a, b} and a < b

(1) The mean of the set is 10.
Many values of {a, b} are possible = {1, 19} or {2, 18} or {2.5, 17.5} so on ...
--> We cannot find exact value of standard deviation --> Insufficient

(2) The range of the set is 10.
--> Many values of {a, b} are possible = {1, 11} or {2, 11} or {2.5, 12.5} so on ...
--> b = 10 + a
--> Set = {a, 10 + a}
Step 1: Mean = (a + 10 + a)/2 = 5 + a
Step 2: Deviations from Mean = {a - (5 + a), 10 + a - (5 + a)} = {-5, 5}
Step 3: Standard deviation = $$\sqrt{\frac{((-5)^2 + 5^2)}{2}} = \sqrt{\frac{50}{2}}= 5$$ --> Sufficient

IMO Option B
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Joined: 10 Jun 2019
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Re: Set V consists of 2 distinct positive values. What is the standard dev  [#permalink]

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02 Nov 2019, 05:41
Statement 1 : the mean alone provides us insufficient information to find the SD

Statement 2 : Every set of 2 distinct numbers with a range of 10 will have the same SD=25. Sufficient
Re: Set V consists of 2 distinct positive values. What is the standard dev   [#permalink] 02 Nov 2019, 05:41
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