Population Distributions

In our statistics class, we have begun to move into the realm of distribution parameters and describing data for management purposes. We were discussing how standard deviations could be used to approximate distributions and probabilities of occurrences with appropriate assumptions. CFA candidates will immediately perk up and remember concepts like Chebyshev's inequality, which describes the percentage of a population which lies within k standard deviations regardless of the underlying population by the formula:

(1 - k^-2) * 100%

k = 2 --> 75%
k = 3 --> 89%

Or more common normal distributions where:
1 σ = 68%
2 σ = 95%
3 σ = 99%
(values shown above are 'expected knowledge' for MBAs and slightly oversimplified)

However, like the CFA exam, I anticipate that the trick in demonstrating an understanding of this concept will be more related to picking appropriate bounds rather than the pure memorization of the percentages for different values of sigma. For instance, in our stats class, we had a problem where we needed to know the probability that our value would not fall below 1 σ. As a clue, that indicates that we need to do a 'one-tailed' test. It is important not to fall into the trap of saying "I see 1 σ, therefore the answer is 68%". In this case, the answer is:
100% - ((100% - 68%) / 2)
100% - (32% / 2)
100% - 16%
= 84%
because it is only a one tailed test.

I have always loved stats. Not just for the pure math value, but more importantly, when trying to prove when math (or anything else for that matter) works or doesn't work, stats is the first place people should go to to determine correlations as a precursor to causality.