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

Question

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.

IanStewart · Answer

Using Statement 1 alone, we'll get the smallest standard deviation when the numbers in the set are as close together as possible. So here, we'll get the smallest standard deviation when the five numbers are consecutive even integers. We now need to know whether the standard deviation of five consecutive even integers is greater than 2. Since GMAT test takers are never expected to compute standard deviations, there's no reasonable way a test taker could know the answer to that question (if every value was a distance of 2 or more from the mean, the standard deviation would be 2 or more, but in a set of five consecutive even integers, one of the values will equal the mean, so that won't be true). It turns out the standard deviation of five consecutive even integers is √8 ~ 2.8, so Statement 1 is sufficient, but it seems out of GMAT scope to me.

Since Statement 2 is clearly not sufficient, the answer is A.

Since Statement 2 is clearly not sufficient, the answer is A.

asishron29181 · Answer

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.

Set cannot consist same elements and all are even numbers.
Let us take an example of set {2,4,6,8,10}
Mean of set = 6
Approx. SD of set = 4+2+0+2+4/5 = 12/5 = 2.4
SD is greater than 2 for set of consecutive even integers.

Let us take another set as {2,6,10,14,18}
Mean of the set = 10
Approx. SD of the set = 8+4+0+8+4 / 5= 24/5 = 4.8
Again SD is greater than 2.
Statement 1 is sufficient.

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

Set consists of 5 items.
Let set be {10,10,10,10,10}
SD of set = 0

Let another set be {10,12,14,16,18}
Mean = 14
SD approx. = 2.4

Clearly contrasting values. 
Not sufficient.

IMO A

sumitkrocks · Answer

Statement (1) All the items in Set P are different even numbers between 1 and 19.
in a set of consecutive even integers which would give the set which is minimum spread out i.e one element equal to mean and rest 4 are at distance of 2 and 4 each 2 respectively .. SD will be  \sqrt{\frac{2*2^2 + 2*4^2 + 0 }{ 5}}  =2 \sqrt{2}  i.e more than 2

Sufficient

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

(A) is the answer IMO

HarshaBujji · Answer

SD= ∑ ∣x−μ∣ ^2/N Where ∑ means "sum of", x is a value in the data set, μ is the mean of the data set, and N is the number of data points in the population. Logic: SD will be minimum for items close to mean/close to each other. If items are spread away from the mean then SD is Max. So to say SD is always >2 we need to just prove it's minimum >2. We need to conclusively prove SD >2 in all the cases of the selected set. Statement 1: All the items in Set P are different even numbers between 1 and 19. According to the above logic we will pick set with close items : {2,4,6,8,10} Avg/Mean = 6 and SD = \sqrt{8} >2 Hence using A we can prove SD will be >2. Hold on !! We need to check another statement as well. Statement 2: The smallest number in the set is 10 So to find Min SD the set should be {10,11,12,13,14} with SD \sqrt{2}<2 But we need to check Max condition as well, If even Max<2 then we can solve this by using Stmt 2. To find Max set should be {10,11,12,19,20} with SD clearly SD>2. Hence it is not consistent and Stmt 2 is not useful. Hence A is a perfect choice. Note: Although this seems lengthy, once we understand it and with mental calculation, it can be done in <2min

TarunKumar1234 · Answer

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

Stat1: All the items in Set P are different even numbers between 1 and 19.
\(p_{min}\) ={2,4,6,8,10}, \(mean_{min}\) = 6, \(SD_{min}\) = \(\sqrt{40/5}\) = 2\(\sqrt{2}\) >2. Sufficient

Stat2: The smallest number in the set is 10.
p can have same 10 as numbers or different nos. Not Sufficient

So, I think A.

Showmeyaa · Answer

1) The minimum SD =  \sqrt{\frac{40}{5}} = 2\sqrt{3}  > 2. Sufficient!
2) The smallest number = 10
Case1: P = {10, 10, 10, 10, 10}, SD = 0
Case2: P = {10, 12, 14, 16, 18}, SD! = 0 Insufficient!, 
Option (C) is a classic GMAT trap!
 (A) IMO!

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

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

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