Set M contains seven integers and set N contains three values chosen f

Question

Set M contains seven consecutive integers and set N contains three values chosen from set M. Is the standard deviation of set N greater than the standard deviation of set M?

(1) Set N contains the median of set M.
(2) The range of set M and set N are equal.

jabhatta2 · Answer

Hi  avigutman   Bunuel  - this is from MGMAT.

I selected (c) for this but the OA is (b)

my set with 7 integers was : (A) {1,2,3,4,5,6,7}

For S2 - i thought about these scenarios

I thought the standard deviations in  (i), (ii) and (iii)  would be very different.

Thus - i thought the standard deviations in  (i), (ii) and (iii)  would MOST LIKELY BE higher / lower than the standard deviation of Set (A) (in the red)

Thus (S2) would not be sufficieint

jabhatta2 · Answer

^^^ avigutman   Bunuel

My thoughts

using excel - i was surprised that the standard deviation of  (i), (ii) and (iii) {in the blue above}  is HIGHER EVERYTIME compared to the standard deviation of  set A (in the red) 
 
 Not sure why if you have fewer elements within the same ranged set --> the standard deviation INCREASES, not decreases

avigutman · Answer

jabhatta2  it would be helpful if you could articulate why you expected what you expected.

Posted from my mobile device

av1901 · Answer

Let M = {1,2,3,4,5,6,7}
Mean(M) = 4
Variance =  /7 = 4
SD(M) = Root(Variance) = 2

Set N contains 3 values, all taken from Set M
Is SD(N) > 2? Or Is Variance(N) > 4?

(1) Set N contains the median of set M.

If N = {1,4,7}: 
Mean = 4
Variance =  /3 = 6
SD(N) is greater than SD(M)

If N = {2,4,6}
Mean = 4
Variance =  /3 = 8/3
SD(N) is less than SD(M)

Not sufficient

(2) The range of set M and set N are equal.

Range of N = 6 which means that N has to contain elements 1 and 7
Which leaves us to the last element
Let us consider the 3 possible cases of different SD

Case 1: 3rd element = 2, Mean=3.33
Variance =  /3 = 6.88

Case 2: 3rd element = 3, Mean=3.66
Variance =  /3 = 6.22

Case 3: 3rd element= 4, Mean=4
Variance =  /3 = 6

Rest will be same as Case 1, 2 and 3

So SD(M) < SD(N) for every case 
Sufficient

Answer - B

Posted from my mobile device

jabhatta2 · Answer

Hi  avigutman  - i said what i said in the yellow highlight  because  standard deviation is a 'spread' from the mean

Here was my thinking

Set A  has  more  elements that are away from the mean

When it comes to  (i), (ii) and (iii)  -- there are fewer elements (within the same range) away from the mean. Thus I thought the SD must be smaller too.

I don't see how one can conclude without calculating the variance to know if 
(a) is the SD higher or lower between Set A and Set (i) or Set (ii) or Set (iii) 
(b) how much does SD move if you eliminate elements (is the movement a big change or a small change) ?

I thought (S2) was not sufficient BECAUSE i thought this maybe was going on

Perhaps in  set (i)  -- the SD is higher than the SD of Set (A) 
 whereas in
 set (ii)  and  set (iii)  -- the SD is lower than the SD of  Set A

Not sure

avigutman · Answer

jabhatta2  Standard deviation is not a 'spread' from the mean. Rather, it's the 'average spread per term', so, conceptually, imagine adding up all the deviations from the mean and  dividing that sum by the number of terms  (this is not going to give you the true SD, but it's an approximation that works great for GMAT purposes).
How I think through statement (2) in this problem:
we have the same range, but fewer terms. This means that the terms that were removed are terms whose deviations were smaller, while the terms with the greatest deviations (the smallest and largest terms) remain. Therefore,  on average , the SD must increase.

Edited to add an analogy:
Class M has seven students, whose heights are all different. Three of those students are chosen to form Group N. Is the average height of the students in Group N greater than the average height of the students in Class M?
(1) ...
(2) The two tallest students in class M are members of Group N.

pappal · Answer

since given 7 consecutive integers in set M and any 03 chosen values from M are in set N
1: states that N contains the median (or mean) of set M, however not sure of the other values in set N. so not sure about its standard deviation.
2: states that the range of both the sets is same, thus easy to say that smallest and the largest values are same in both the sets.
thus choosing any third value of set N. the values in set N will be more sparsely distributed about mean than in set M. Hence SD(N)> SD(M)
SUFFICIENT
B is the correct choice.

Set M contains seven integers and set N contains three values chosen f

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GMAT Data Sufficiency (DS) Questions

Set M contains seven integers and set N contains three values chosen f

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