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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.

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

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.

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?

Z - X = 10 implies that Z is greater than X by 10 which means Z MUST be to the right of X on the number line. It doesn't matter whether Z and X are both positive, both negative or one positive one negative. You cannot put Z to the left of X on the number line and still have Z - X = 10. This is the reason using number line is a good idea because it gives you a lot of clarity.
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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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I would say 650 - 700. Note that there are certain complications:

1. The concept of SD is not very intuitive to many people which makes this question hard. Once you understand it, you feel its simple. 2. X, Y and Z are not given to be positive so subtraction puts people off sometimes since they feel they have to account for positive as well as negative numbers. Its all in the perception.
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Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]

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17 Jan 2013, 06:46

Bunuel wrote:

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.

Sweet Trick to solve the question, very helpful!
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Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]

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23 Jan 2013, 06:36

fozzzy wrote:

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

1. From the information we know that the gap between Z and X is 10 so we can think of any number with that gap... {5,Y,15} or {10,Y,20} or {50,Y,60}, etc. These sets are similar to the given {10,15,20} in such away that the first and last term are of a distance of 10.

Notice that the middle number of {10,15,20} is 15 which is equal to the average = 20+10+15/3 = 15. Now, we do not know the middle number or Y or {X,Y,Z}. If Y is equal to the average then it will have an SD equal to the SD of {10,15,20}. If Y is not equal to the average, then our SD will be greater.

INSUFFICIENT!

2. From the information we know that Y and Z are of 5 away from each other {X,15,20} or {X,16,21}, etc. These sets are similar to {10,15,20} in terms of the distance of 2nd to the last term. But, we need to know X to know how spread out are the numbers. If X -Y is 5 then the SD will be the same. If not then the SD will not be the same.

INSUFFICIENT!

Together: {X,Y,Z} = {i, i+5, i+10} SD is the same with {10,15,20} where i=10: {10, 10+5, 10+10}

Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]

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17 Mar 2013, 01:05

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?
_________________

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Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]

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13 May 2014, 05:47

Hello from the GMAT Club BumpBot!

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Re: Is the standard deviation of the numbers X, Y and Z equal to [#permalink]

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18 Oct 2015, 03:06

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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