- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 7. Chebyshev's Inequality
CFA Practice Question
There are 410 practice questions for this study session.
CFA Practice Question
It has been determined that the mean return rate for tax-exempt municipal bonds is 9.2% with a standard deviation of 3%. What is the minimum percentage of return rates for tax-exempt municipal bonds with rates between 4.7% and 13.7%?
Correct Answer: A
Since 13.7% is 1.5 standard deviations above the mean of 9.2% and 4.7% is 1.5 standard deviations below the mean of 9.2%, we would expect at least 1 - 1/1.52 = 0.56 of the rates to fall within this range (Chebyshev's Inequality).
User Contributed Comments 10
|chuong||9.2% + 1.5x3%=13.7%
9.2% -1.5x3% = 4.7%
Chebyshev's Inequality defines how many values are within C standard deviation. So here it means that at least 56% of the total data set values are lying between interest rates 4.7% and 13.7%.
|TammTamm||Did the 1.5 come from 3/2?|
|Nuta||1.5 = (13.7-9.2)/3|
|Sabs||or 1.5 = (9.2-4.7)/3|
|skath||If the questions mentions the word "between" then you can SD/2.|
|johntan1979||I know you can't determine the 1.5 sd from the empirical rule, but what if it is 2 sd? When do we use the empirical rule (95%) vs Chebyshev's (75%)?|
|johntan1979||Think I found the answer myself, which is to examine the answer options. Tricky, if you are like me, automatically apply the empirical rule.|
|sgossett86||1 sd is 66%, so why would 1.5sd be less than 66%? couldn't we do something like 1.5 * .66 to solve ? I am not relying on you guys for the answer. I'm trying to make this make sense to me better. I guess if the empirical rule is used only for normal distributions, which basically never occur, we're using this law to evaluate all other distributions, so i guess it makes sense in that regard.|
|msk500||Simply, the mean return = 9.2. Anything below or above this mean deviates from the mean. So, if a return is 4.7, then it is 4.5 less than the mean of 9.2. If every (ie 1) deviation is 3, then 4.5 deviations = 1.5 standard deviations. Similarly, if a return is 13.7, then this is 4.5 deviations above the mean, and a standard deviation of 1.5. Applying Chebychev's inequality, you get 1-(1/1.5^2) = 0.555556 or 56%.|