Problem Solving

If d is the standard deviation of x, y, 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

OG answer is A.

Can anyone explaine please?

The only factors relevant to standard deviation is the number of terms and the spacing of the terms - the actual value of the terms is irrelevant.

So, if all we're doing is shifting all the terms in a set to the left or right, the SD will remain constant.

For example, any set of 3 consecutive even numbers will have the same SD.

-as per Stuart

Goes to the flash cards:

1) Adding or subtracting a constant from each element in the set has no effect on standard deviation. Remains the same

In the problem above a constant 5 is added to the elements hence the std deviation remains constant

2) Multiplying the elements of a set with an abolsute value greater than 1 increases the standard deviation

3) Dividing the elements of a set with an abolsute vaue greater than 1 decreases the std deviation

4)Changing the signs of the element of a set or multiplying by -1 has no effect on std deviation.Remains the same

If it helps to illustrate with numbers regarding this question...TRY THIS:
Ex: if X,Y,Z...were three consecutive numbers or any set of numbers that you know standard deviation...I piked X,Y,Z to be 1,2,3 so standard deviation is of 1,2,3 is 1 (which is d as liste din the question). Since they are 1 apart when graphed.

So,adding to 5 to each set of numbers results in 6,7,8...again(you can see that standard deviation remains the same) so the answer remain d, which is your answer

cramya wrote:Goes to the flash cards:

1) Adding or subtracting a constant from each element in the set has no effect on standard deviation. Remains the same

In the problem above a constant 5 is added to the elements hence the std deviation remains constant

2) Multiplying the elements of a set with an abolsute value greater than 1 increases the standard deviation

3) Dividing the elements of a set with an abolsute vaue greater than 1 decreases the std deviation

4)Changing the signs of the element of a set or multiplying by -1 has no effect on std deviation.Remains the same

Which set of flashcards are you referring to?

People normally add these points to their own flashcards. That's what she meant. These points are vital to remember during the test day. Make note of these points in your flashcards if you haven't.

great tips to know for test day.

Picking numbers to the above explanations...

If x,y,z equals= 5,10,15 then the std deviation is 5

If you add/increase+5 the std deviation we get= 10,15,20 again the std deviation is 5

Taking the same values of =5,10,15 if we multiply them by 2 we get 10,20,30 and the std deviation is now 10!

luiscarlos59 wrote:Picking numbers to the above explanations...

If x,y,z equals= 5,10,15 then the std deviation is 5

If you add/increase+5 the std deviation we get= 10,15,20 again the std deviation is 5

Taking the same values of =5,10,15 if we multiply them by 2 we get 10,20,30 and the std deviation is now 10!

Hi!

I have some bad news for you and some good news.

The bad news is that your calculation of SD is way off; the SD of {5, 10, 15} is NOT 5.

The good news is that you don't actually need to know how to calculate SD for the GMAT; you merely have to have a basic idea of what SD is and when it's possible to calculate it.

For data sufficiency purposes, you can calculate SD if you know:

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

Of course, if you know the full set, you also know (1) and (2) above.