Problem Solving

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

1.d

2.3d

3.15d

4.d+5

5.d+15.

OA A

I'm assuming that you want an explanation.

use your calculator/excel and see. or google standard deviation

SD measures the spread of the values in the set, hence if all values are increased/decreased by same number the spread does not change.

ie, lets say that you have 10 people standing in a line and they are 1ft apart, you tell all of them to move froward by 5ft, have their spread changed? no, they are all still 1ft apart from each other.

or you can solve it (for you understanding) using SD formula.

SD^2 = ((x1-x)+(x2-x)+(x3-x)+......+(xN-x))/N

where x is the mean of x1,x2,......,xN

take 3 numbers and solve the result will always be the std deviation itself when all terms are added with a constant.

abhinav85 wrote:If the d is the standard deviation of x,y and z,what is the standard deviation of x+5,y+5 and z+5?

1.d

2.3d

3.15d

4.d+5

5.d+15.

OA A

On the GMAT, you never need to actually solve for standard deviation ("SD") using the formula. Here are some SD questions that people have seen:

- given the SD and the mean of a set, which of the following results is between 2 and 3 SDs from the mean? (Seems to be the most common problem solving SD question these days.)

- given 5 different sets, which set has the highest/lowest SD?

- given 5 different graphs, which set has the highest/lowest SD? (Although I haven't heard of that question showing up for quite a while.)

- questions similar to the one you posted.

- in data sufficiency, questions asking what's the SD of a set.

All of these questions require an understanding of the basics of SD, so that's what you should focus on attaining.

SD measure how spread out the terms of a set are from the mean. The more spread out the numbers, the higher the SD.

Any set with more than 1 distinct term will have a SD > 0. If all of the terms in a set are identical, SD = 0.

From a data sufficiency perspective, to solve for SD you need to know two things:

1) the # of terms in the set; and
2) the exact spacing of all of the terms.

If you know the whole set, you know both (1) and (2). However, you don't need to know the actual values to solve for SD. For example, if we knew that our set contained 5 consecutive even integers, we could solve for SD; since {2, 4, 6, 8, 10} and {18, 22, 24, 26, 28} contain the same number of terms and have the exact same spacing, they have the same SD.

Understanding this principle would allow you to answer the question you posted. {x, y, z} and {x+5, y+5, z+5} have the same number of terms and the same spacing, so they have the same SD.

Further, knowing the limitations of what the GMAT tests would have also led you to strategically guess choice A. Since we're not expected to know the SD formula, there's no way the answer could be anything except A, since any other answer would require applying the formula in some way.

thanx a tonn stuart...
i always had doubts in SD....

many things got cleared.

Regards
Arun

Thanx Stuart.......