Chebyshev's Theorem

Question

What is difference between taking the lower bound and lower limit from Chebyshev's Theorem?

If P(|Y- mean|) <= 1 - (1/r^2)

Do we have to consider 1 - (1/r^2) as the lower bound?

Answer 1

Lower bound and lower limit can be used interchangeably, what Chebyshev's theorem states is that the proportion of observations can be no less than (1-1/k²) where k relates to the number of standard deviations you are from the mean.

So however many standard deviations (k) you are from the mean, the minimum proportion or percentage of the data that must be contained in the dataset can be found by ≤(1-1/k²)