# Chebyshev inequality

According to Chebyshevs inequality, the minimum proportion of observations falling within 3 standard deviations of the mean for a negatively skewed distribution is closet to: a 56% b 68% c 75% d 89%

the answer is D

i thought so too, but thats not what the answer book says…

which book?

SS Book 6, Exam 2 Morning session Q 28.

yeah i saw that too…it says the answer is C. 75% But when i read the CFA notes it states Vol 1 pg. 288 “a three standard deviation interval around the mean must contain at least 89% of the observations, no matter how they are distributed.” I would take the CFA notes over schweser notes anyday.

It’s D for sure.

I got this: Exam Review - Question 28 Question ID#: 45117 Your answer: D was correct! According to Chebyshev’s inequality, the proportion of the observations within 3, which is k, standard deviations of the mean is at least 1 - (1/k^2) = 1 - (1 / 3^2) = 0.89 or 89%. This holds for any distribution, regardless of the shape. It’s probably in one of the errata postings on Schweser website. _________ I looked it up: these are the wrong answers in book 6: Exam, Q, Wrong, Right 1PM 79 A C 2AM 25 A B 2AM 28 C D 2AM 120 D C 2PM 87 B D 3PM 21 A B

yea, the answer key is wrong. However if you look at the solution set with detailed explanations, it is calculated as 88.88% So I guess its just a printing mistake

it has to be D.

Thanks all, at least i am not going nuts (yet).

it has to be D, schweser probably had a typo, here’s how - 1-1/k^2 = 1-(1/9) = 1-.11111 = .89