Mar 9 2026
The Language of Money for Engineers and Managers
This is a primer for engineers and operations managers who are hazy about concepts such as the time value of money, discounted cash flow (DCF), net present value (NPV), or internal rate of return (IRR). It is meant to level the playing field for them when dealing with MBAs to whom it’s “Business 101.”
Apr 3 2026
Deviating Standard Deviations
This basic concept deserves revisiting. The following is from a blog post from 2022 hosted by a supplier of statistical software intended to explain the meaning of some notations in plain, simple terms:
The author calls two different things by the same name. If the standard deviation of each variable is 1, how could its expected value be anything else? The confusion within this nonsensical statement is the same we make when we equate the temperature of a soup with a thermometer reading. In our mental model of a bowl of soup, it has a temperature that exists regardless of our ability to measure it, and the thermometer reading is only an estimate of it.
For the purposes of eating soup, confusing the two is harmless, unless the thermometer, poorly calibrated, always gives you an answer that is 15°F off. This is the situation we have with the most commonly used estimator of the standard deviation of a random variable from a small sample. It is biased, and c_4(n) is a correction factor applicable when the random variable is Gaussian.
To describe c_4(N) accurately, we need to dig into probability theory. It is, in fact, the expected value of the estimator S=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}\left ( X_i -\bar{X} \right )} of the standard deviation from a sample of N independent Gaussian variables \left ( X_1, \dots, X_N \right ) with unit standard deviation, \sigma = 1. This is an accurate statement, but every term in it needs an explanation.
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By Michel Baudin • Technology 0 • Tags: Control Charts, Probability, Quality, Six Sigma, SPC, Standard Deviation, statistics