Chebyshev's Inequality-Please explain

CFA Level I
#1

Could someone please explain the formula to me. I know it’s 1-1/k^2 but if you subtract 1-1 that’s zero. If there are 3 standard deviations how can the answer be 89%? 1-1=0 0/3^2=0 How can 0 be divided to get a percentage? Any help will be appreciated.

#2

it is applicable only if k > 1

#3

k has to be >1, that’s a condition under Chebyshev.

#4

Please explain more. So with 3 standard deviations, how is the answer 89%? This was on the CFAI sample exam I just took. Am I missing something?

#5

The formula is 1-(1/k^2). If k = 3 then : 1-(1/9)=0.89 = 89%

#6

u got the parentheses wrong 1 - (1/k^2) If 3 Std Dev: 1 - (1/9) = 1 - 0.1111 = .888 ~ 89%

#7

Thanks, everyone because in SS2 Reading 7, page 289 & 290 the equation is listed as 1-1/k^2 & 1-1/(1.25)^2

#8

1-1/k^2 is correct because of something called operator precedence…divide comes before “-”.

#9

PEMDAS anyone? Order of Operations - Paranthesis Exponents Multiplication Division Addition Subtraction

#10

wow…

#11

=)

#12

Please Excuse My Dear Aunt Sally… never thought I’d say that again!