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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

Attachment: PS8.PNG [ 8.1 KiB | Viewed 26488 times ]

Originally posted by LM on 10 May 2010, 08:37.
Last edited by Bunuel on 26 Nov 2018, 03:41, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert V
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If d is the standard deviation x, y, and z, what is the standard devia  [#permalink]

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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.

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Re: If d is the standard deviation x, y, and z, what is the standard devia  [#permalink]

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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.

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Re: If d is the standard deviation x, y, and z, what is the standard devia  [#permalink]

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LM wrote:
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

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

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Re: If d is the standard deviation x, y, and z, what is the standard devia  [#permalink]

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LM wrote:
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

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.

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Re: If d is the standard deviation x, y, and z, what is the standard devia  [#permalink]

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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.

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.

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Re: If d is the standard deviation of x, y, and z , what is the  [#permalink]

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_________________ Re: If d is the standard deviation of x, y, and z , what is the   [#permalink] 08 Oct 2019, 06:46
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