- 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**

Which of the following is incorrect?

A. The sum of deviations from the mean always equals zero.

B. For a sample, the mean absolute deviation can never be equal to the standard deviation.

C. A t-distribution does not have a finite standard deviation.

**Explanation:**Mean absolute deviation will be equal to standard deviation for a sample with an equal number of two discrete values (all deviations of equal magnitude, half positive and half negative). In other situations standard deviation will exceed mean absolute deviation.

###
**User Contributed Comments**
4

User |
Comment |
---|---|

czar |
why? |

toyo |
Could anyone show example? |

simonbenfrech |
Example: 4 observations and Standard deviation computed as a population(n) one and not a sample one (n-1) 10,10,0,0 Mean =20/4 = 5 MAD = (5+5+5+5)/4= 5 VARIANCE = (25 *4)/4 = 100/4= 25 Std.Dev = 25^(0.5) = 5 CQFD MAD = Std. Dev |

Vlz2103 |
When all the numbers of a distribution are the same all measures of variance are 0...although simon's example is better lol. |