CFA Practice Question

There are 410 practice questions for this study session.

CFA Practice Question

A random variable, X, has a mean of 12 and a standard deviation of 14. If another variable, Y, is defined by Y = 2X - 3, the coefficient of variation of Y is ______.
A. 0.75
B. 1.33
C. 1.19
Explanation: You should remember two important points:
  • Multiplying a random variable by a constant multiplies its mean and standard deviation by the same constant.
  • Adding a constant to a random variable increases the mean by the same constant but leaves the standard deviation unchanged.
Using these two rules, the mean of Y equals 2 * 12 - 3 = 21. The standard deviation of Y equals 2 * 14 = 28. The coefficient of variation equals the ratio of the standard deviation to the mean. Thus, the coefficient of variation of Y equals 28 / 21 = 1.33.

User Contributed Comments 6

User Comment
Goran80 Coefficient of variation of Y is standart deviation((X) / mean (X).
rebecca07 Sorry, pleas help. I dont really get this. Thanks!
fiesta How do you get standard deviation of Y...shouldn't you subtract three from 28? Thanks
JimM Standard deviation is not changed when a constant is added or subtracted to the numbers. It is changed when the numbers (values) are multiplied by a constant. The mean is adjusted by both.

So, new mean = 2*old - 3 = 21.
And, new std dev = 2*old = 28.

coeff variation = std dev / mean = 28 / 21 = 1.33
migena thanks a lot JimM!!
navarro Wao, can someone please explain this to me? I am having a lot of trouble understanding it.
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