- 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**

Using Chebyshev's Inequality, what is the minimum proportion of observations from a population of 500 that must lie within two standard deviations of the mean, regardless of the shape of the distribution?

B. 75%

C. 85%

A. 66%

B. 75%

C. 85%

Correct Answer: B

Chebyshev's inequality holds for any distribution, regardless of shape, and states that the minimum proportion of observations located within k standard deviations of the mean is equal to 1 - 1/k

^{2}. In this case, k = 2 and 1 - 1/4 = 0.75 or 75%.###
**User Contributed Comments**
2

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

carbonro |
if we're calculating 2 sd here, why wouldn't we calculate 3 sd in problem 1 as opposed to 1.5? |

amagegbai1 |
Carbonro, I guess its because if we were not given a "base" mean and range of means as in between 4.7% and 13.7% as in the previous question which we can divide by the SD. Logic also tells that if we divide the SD in this question by 2 we will end up having 1 which Chebyshev's theorem doesn't quite apply.... |