Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10, 15 and 20?

(1) Z - X = 10. No info about y. Not sufficient.
(2) Z - Y = 5. . No info about x. Not sufficient.

(1)+(2) From above x = z - 10 and y = z - 5, so the set in ascending order is {z-10, z-5, z}. Now, if we add or subtract a constant to each term in a set the standard deviation will not change. Adding 20-z to each term in the set we get {10, 15, 20}. So, the standard deviation of {z-10, z-5, z} is equal to that of {10, 15, 20}. Sufficient.

Answer: C.

Hope it's clear.
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Another way to look at SD is to think in terms of a number line. SD calculates the dispersion of numbers from the mean. The SD of two sets will be the same if the relative placement of numbers from the respective means is the same.

This is what 10, 15 and 20 will look like on a number line
10 .... 15 .... 20
(15 is the mean and 10 and 20 are 5 steps away from the mean. Each dot is a number between 10 and 15 and between 15 and 20)

(1) Z - X = 10
This is what Z and X will look like on the number line
X ......... Z

(2) Z - Y = 5
This is what Z and Y will look like on the number line
Y .... Z

Together, their relative placement on the number line looks like this:
X .... Y .... Z

This matches the placement of 10, 15 and 20 and hence the SD will be the same in the two cases.

For more on number line concepts of SD, check: http://www.veritasprep.com/blog/2012/06 ... deviation/
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well I thought the same way and was going to mark C
But I stopped thinking of another case

Y....Z.........X
I.e this case satisfies the 2 conditions difference between Y and Z is 5 and difference between Z and X is 10, will SD be same in this case too?
Sounds a bit stupid, but need to know why this approach is incorrect?

Also, SD of 10, 15, 20 will not be the same as SD of Y....Z.........X (e.g. 5, 10, 20). The distance of the numbers from the mean is not the same in the two cases.

SD of 10, 15, 20 will be the same as SD of 20, 25, 30 or of 41, 46, 51 or of -16, -11, -6 etc.
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Is the 700-level rating accurate?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the standard deviation of the numbers X, Y and Z equal to the standard deviation of 10,15 and 20?

(1) Z - X = 10
(2) Z - Y = 5

Looking at the original condition, there are 3 variables (x,y,z) and in order to match the number of variables and equations, we need 3 equations. However, only 2 equations are given from the 2 conditions, so there is high chance (E) will be our answer
Looking at the conditions together,
In 10,15,20, there are differences of 5 between 10&15, 15&20, but a difference of 10 between 10 and 20.
According to x,y,z, there is a difference of 5 between x and y, and also 5 between y and z, and 10 between z and x. The standard deviation becomes identical, and therefore the conditions are sufficient, making the answer (C)

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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If y = -5 and z = -10 then Z - Y = -5, not 5.

Also, most of the solutions above deal with the problem conceptually, which includes all cases.
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Hi All,

While this question requires some specific knowledge about Standard Deviation, you don't actually have to do much math to solve it. To start, it's worth noting that the GMAT will NEVER ask you to calculate the Standard Deviation of a group using the S.D. formula, so that is NOT what this question is actually about.

We're asked if the S.D. of three numbers (X, Y and Z) is the SAME S.D. as the one for the numbers 10, 15 and 20. This is a YES/NO question.

The numbers 10, 15 and 20 are 'evenly spaced' numbers that differ by 5. To have the same S.D. as this group, another group must ALSO have evenly spaced numbers that differ by 5. For example, (0, 5, 10) and (1, 6, 11) would have the same S.D. as (10 15. 20).

1) Z - X = 10

This Fact fits part of the pattern that we're looking for, but we don't know the relative value of Y.
Fact 1 is INSUFFICIENT

2) Z - Y = 5

This Fact also fits part of the pattern that we're looking for, but we don't know the relative value of X.
Fact 2 is INSUFFICIENT

Combined, we know....
Z - X = 10
Z - Y = 5

This means that Z is the largest value, that Z is 5 greater than Y, and that Z is 10 greater than X. By extension, Y would then be 5 greater than X. This is an exact match for the 'spread' created by (10, 15, 20), so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Yes, if we add or subtract a constant to each term in a set the standard deviation will not change. If we subtract 30 from each term in {40 , 45 , 50} we get {10, 15, 20}, so the SD of these two sets are the same.
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.


Since we have 3 variables and 0 equations, E is most likely to be the answer and so we should consider 1) & 2) first.

The distance 10 and 20 is 10 and the distance 15 and 20 is 5.
The distance X and Z is 10 and the distance Y and Z is 5.
Since the distributions of two data sets are same, their standard deviations are same.
Both conditions 1) & 2) are sufficient.

Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A).

Condition 1)
Since we don't know anything about Y, this is not sufficient.

Condition 2)
Since we don't know anything about X, this is not sufficient.

Therefore, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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