- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 7. Chebyshev's Inequality

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**CFA Practice Question**

An investment has a mean return of 15% with a standard deviation of 4.5%. You expect that 75% of the rates will fall within which values?

A. 5.9%; 24.9%

B. 6.0%; 24.0%

C. 6.2%; 24.0%

**Explanation:**75% corresponds to k=2 because 0.75 = 1 - 1/2

^{2}. Therefore, the extremes for the interval are 15% +- 2 * (4.5%) or 6% and 24% (Chebyshev's Inequality).

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**User Contributed Comments**
9

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

seanny00 |
When would you use Chebyshev's inequality vs. a z-value? The z value gives you a different result in this case. |

Peter |
you can use the z value only if you're sure that the distribution is normal. in this case there is no mention of that so you have to use the Ch. inequality. |

surob |
or if N>=30 |

kellyyang |
yes! this is very tricky question. I don't understand either why needs to use Chebyshev's ? Does anyone knows why? |

bhavini |
thanks Peter. I was getting confused why they were not using z table here. |

showmethemoney |
Ch inequality applies to any distribution |

jonan203 |
@kelly if, for example, the question asked for what % of rates fall 1.4 deviations from the mean you would use c-inequality as follows: 1 - (1/1.4^2) = 48.98% |

tmeeker |
When in doubt, verify if the answers make sense. B is the only answer that makes sense: A. 15 +/- X = 5.9 or 24.9 (range is + 9.9 but - 9.1) B. 15 +/- X = 6 or 24 (range is +/- 9) C. 15 +/- X = 6.2 or 24 (range is + 9 but - 8.8) If there is no skew mentioned, the range should be the same in each direction: B. |

sloriot |
I thought we had to multiply with standard error.. not just standard deviation in order to get the conficence interval |