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SD

by sindhujah_kk » Thu Oct 28, 2010 11:29 pm
Set A is a set of consecutive integers from 1 to 100. Set B is obtained by multiplying each integer in set A by 2. Set C is obtained by multiplying each integer in Set a by -3. Set D is obtained by adding 3 to each no of set A. Which of the following is correct ordering of SD from least to greatest?

A) BCD
B) CDB
C) DBC
D) DCB

Please help.Would like to know how SD changes by multiplying with a -ve number.
Thanks
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by Rahul@gurome » Thu Oct 28, 2010 11:52 pm
sindhujah_kk wrote:Set A is a set of consecutive integers from 1 to 100. Set B is obtained by multiplying each integer in set A by 2. Set C is obtained by multiplying each integer in Set a by -3. Set D is obtained by adding 3 to each no of set A. Which of the following is correct ordering of SD from least to greatest?

A) BCD
B) CDB
C) DBC
D) DCB

Please help.Would like to know how SD changes by multiplying with a -ve number.
Thanks
The standard deviation is invariant to changes in location, and scales directly with the scale of the random variable. Thus, for a constant c and random variable X:
(1) SD(X + c) = SD(X)
(2) SD(c*X) = |c|*SD(X)

For this problem,
SD(B) = SD(2A) = 2*SD(A)
SD(C) = SD(-3A) = 3*SD(A)
SD(D) = SD(A + 3) = SD(A)

Thus, SD(D) < SD(B) <SD(C)

The correct answer is C.
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by Rezinka » Sat Oct 30, 2010 2:00 am
SD does not depend on negative or positive but on magnitude.
Suppose,
you had another set E obtained by multiplying set A by 4, then set E would have SD higher than set C.
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