If d is the standard deviation x, y, and z, what is the standard devia

Question

If d is the standard deviation x, y, and z, what is the standard deviation of x + 5, y + 5, z + 5 ? A. d B. 3d C. 15d D. d + 5 E. d + 15 PS8.PNG

Bunuel · Accepted Answer

If d is the standard deviation x, y, and z, what is the standard deviation of x+5, y+5, z+5

A. d
B. 3d
C. 15d
D. d+5
E. d+15

TIP:
If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

So in our case SD won't change as we are adding 5 to each term in a set --> SD=d.

Answer: A.

More about standard deviation:
https://gmatclub.com/forum/math-standard ... 87905.html
https://gmatclub.com/forum/ds-questions- ... 85896.html
https://gmatclub.com/forum/ps-questions- ... 85897.html

AbhayPrasanna · Answer

This is conceptual. Standard deviation is a measure of the difference between each value in a set and its mean value.

Now, if x,y and z have a standard deviation of d, this indicates to us that the average deviation of x,y and z from the mean of x,y and z is d.

If we simply shift the entire set of x,y and z along the number line by a quantity of 5, does this alter the amount by which they will vary around their new mean? No, their deviation relative to their mean will not change, as the mean itself has moved correspondingly, maintaining the same differences for x+5, y+5 and z+5. Thus the standard deviation will remain unchanged.

Pick A.

BrentGMATPrepNow · Answer

Adding the same value to each value in a set does not change the standard deviation of the set.

So, the standard deviation of {x + 5, y + 5, z + 5 } will also be d.

Answer: A

GMATinsight · Answer

CONCEPT  : Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.

1) It depends on the separation between the successive terms of the set

2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1 + 10, 2 + 10, 3 + 10, 4 + 10, 5 + 10}

3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}

When 5 is added in each term of set {x, y, z} then the new set {x+5, y+5, z+5} will remain same as the previous standard deviation i.e. d

Answer: Option A

ScottTargetTestPrep · Answer

In a data set, if every number is increased (or decreased) by the same amount, the standard deviation of the data set will not be affected. That is, the new standard deviation is still equal to the original standard deviation. Here we see that each data value is increased by the same amount (5 in this case); therefore, the standard deviation will still be d.
 
Answer: A

EMPOWERgmatRichC · Answer

Hi All,

In real basic terms, Standard Deviation is a measure of how "spread out" a group of numbers is. Numbers that are "close together" will create a small Standard Deviation, while numbers that are really "spread out" will create a large Standard Deviation.

Here, we have 3 values: X, Y and Z. We're told that they have a Standard Deviation of D.

To help you visualize what's going on here, let's TEST VALUES…

X = 1 
Y = 2 
Z = 3 
Standard Deviation = D (don't worry about calculating it, the GMAT will NEVER ask you to calculate a Standard Deviation)

Notice the "spread" of the above numbers; we'll come back to this in a moment.

The question then asks us to think about X+5, Y+5 and Z+5. Using the values from above, we would have…. 
1+5 = 6 
2+5 = 7 
3+5 = 8

Now, notice how these values have the exact SAME SPREAD as the initial set of numbers? This group of numbers has the SAME STANDARD DEVIATION as the original set of numbers. Thus, the Stand Deviation is still D.

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

COolguy101 · Answer

Similar to this one, 
 If x is the standard deviation of a, b, c, d, e, and y is the standard deviation of a-3, b-2, c, d+2, e+3.
which one is greater?  Bunuel  sir

EMPOWERgmatRichC · Answer

Hi COolguy101,

The answer to your question will depend on the relative values of A, B, C, D and E (since increasing/decreasing a value can have a distinct effect on the S.D. of the entire group).

For example:

IF.... A = B = C = D = E = 3, then...
the first group is {3, 3, 3, 3, 3}
the second group is {0, 1, 3, 5, 6}

Here, the the S.D. of the first group would be 0 (since all 5 values are the same) and the S.D. of the second group would be larger.

However,

IF.... A = 3, B = 2, C = 0, D = -2, E = -3, then....
the first group is {3, 2, 0, -2, -3}
the second group is {0, 0, 0, 0, 0}

Here, the the S.D. of the second group would be 0 (since all 5 values are the same) and the S.D. of the first group would be larger.

GMAT assassins aren't born, they're made,
Rich

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If d is the standard deviation x, y, and z, what is the standard devia

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