Set A = {1, 2, 3, 4, 5, 6, y} Which of the following possible values

Question

Set A = {1, 2, 3, 4, 5, 6, y}

Which of the following possible values for y would cause Set A to have the smallest standard deviation?

A. 1
B. 2.5
C. 3
D. 3.5
E. 7

GMATinsight · Answer

P.S. Standard Deviation would Increase if the new value is at a larger deviation from mean than the standard deviation of the set on the contrary the standard deviation would be least if the values are closer to the mean of the set

for given 6 values {1, 2, 3, 4, 5, 6} the mean is 3.5 hence the value that we must take should be Closest from the mean in order to have the least possible standard deviation

Out of the option, x = 3.5 will be closest from 3.5 with deviation from mean as zero

Answer: Option D

mohshu · Answer

the mean is 3.5,,, hence closer to the mean gives no change in SD

ans D... 3.5...

GMATinsight · Answer

A little correction/clarification

- A new value included in set which is closer to the mean than the value of standard deviation REDUCES standard deviation

- A new value included in set which is at an equal distance from the mean as the value of standard deviation is causes NO CHANGE standard deviation

- A new value included in set which is at a greater distance from the mean than the value of standard deviation INCREASES the standard deviation

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HKD1710 · Answer

Closer to the mean and lesser the deviation. If equal to the mean then zero deviation. for the set 1,2,3,4,5,6 ---> mean is 3.5 If we add y as 3.5 then there will be no deviation. hence D

BrentGMATPrepNow · Answer

Some background about Standard Deviation on the GMAT
 
For the purposes of the GMAT, it's sufficient to think of Standard Deviation as the  Average Distance from the Mean . Here's what I mean:

Consider these two sets: Set A {7,9,10,14} and set B {1,8,13,18}
The mean of set A = 10 and the mean of set B = 10
How do the Standard Deviations compare? Well, since the numbers in set B deviate the more from the mean than do the numbers in set A, we can see that the standard deviation of set B must be greater than the standard deviation of set A.

Alternatively, let's examine the Average Distance from the Mean for each set.

Set A {7,9,10,14}  
Mean =  10 
7 is a distance of 3 from the mean of  10 
9 is a distance of 1 from the mean of  10 
10 is a distance of 0 from the mean of  10 
14 is a distance of 4 from the mean of  10 
So, the average distance from the mean = (3+1+0+4)/4 =  2

B {1,8,13,18}  
Mean =  10 
1 is a distance of 9 from the mean of  10 
8 is a distance of 2 from the mean of  10 
13 is a distance of 3 from the mean of  10 
18 is a distance of 8 from the mean of  10 
So, the average distance from the mean = (9+2+3+8)/4 =  5.5

IMPORTANT: I'm  not  saying that the Standard Deviation of set A equals 2, and I'm  not  saying that the Standard Deviation of set B equals 5.5 (They are reasonably close however).

What I am saying is that the average distance from the mean can help us see that the standard deviation of set B must be greater than the standard deviation of set A. 
More importantly, the average distance from the mean is a useful way to think of standard deviation. This model is a convenient way to handle most standard deviation questions on the GMAT.

-------------------------------------------------------

In the given question, the set {1, 2, 3, 4, 5, 6} has a mean of 3.5

Our goal is to determine the value of y that, when added to the set" will result in the smallest standard deviation.

If y = 3.5, this new value is a distance of 0 from the mean. 
So, this y-value will result in the new set having the smallest standard deviation.

RELATED VIDEO FROM OUR COURSE
  https://www.youtube.com/watch?v=FbAlIjw2fwY

JeffTargetTestPrep · Answer

Let’s first calculate the mean of the given 6 numbers:

(1 + 2 + 3 + 4 + 5 + 6)/6 = 21/6 = 7/2 = 3.5

We may recall that the closer the values in our set are to the mean, the smaller the standard deviation. Thus, when selecting a value for y, we want to select the value that will be closest to 3.5.

Thus, we see that choice D, 3.5, is correct choice.

Answer: D

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Set A = {1, 2, 3, 4, 5, 6, y} Which of the following possible values

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Set A = {1, 2, 3, 4, 5, 6, y} Which of the following possible values

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