- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions
- Subject 7. The Standard Normal Distribution

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**CFA Practice Question**

A bell-shaped, symmetrical frequency distribution has a mean of 10. If 16% of the observations in the distribution are negative, what is the coefficient of variation of X?

A. 0.1

B. 1.0

C. 10.0

**Explanation:**The fraction of observations that are less than zero equals 16%; i.e., the fraction of observations that are less than (mean - 10) equals 16% (given). Since the distribution is symmetrical about the mean, this implies that the fraction of observations that are more than (mean + 10) also equals 16%. Thus, the fraction of the observations lying between 0 and 20 equals 1-0.16-0.16 = 0.68. For a bell-shaped, symmetrical frequency distribution, 68% of the observations lie within one standard deviation of the mean. Hence, the standard deviation of the distribution equals 10. The coefficient of variation is then equal to standard deviation/mean = 10/10 = 1.

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**User Contributed Comments**
5

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

miso |
Why st dev is 10 not 1 |

PedroEdmundo |
Miso, we have (10-kS;10+kS)=(0;20) and k=1, thus S=10 |

Thecatz |
tricky because it does not say directly that the distribution is normal... |

homersimpson |
20-10/stdv=k, k=1, stdv=10 |

ascruggs92 |
"Bell shaped, symmetrical frequency distribution" implies a normal distribution. Therefore, we know that 68% of all observations are within one Std. Dev. of the mean, and each tail contains 16% of observations (100-68=32%, 32/2=16%). Furthermore, if 16% of observations are negative, 0 must be one std. dev. away from the mean. Then it's just math from there: Std. Dev. = 10 - 0 = 10 Coefficient of Variation = std. dev./mean = 10/10 = 1 |