- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 6. Measures of Dispersion

###
**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.

###
**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. |