A field guide to the most popular parameters | Statistics - Medium

Note: If a concept is new to you, follow the link for my explanation. If the early stuff feels too technical, feel free to skip to the cuddly critter memes lower down.

Get your distribution basics in Part 1 if you’re new to this space.
Image: SOURCE.

Ready for the list of favorites? Let’s dive right in!

Take a “moment” to explore some fundamentals.

This article takes you on a tour of the most popular parameters in statistics! says Cassie Kozyrkov, Head of Decision Intelligence, Google, published in Towards Data Science.

If you’re not sure what a statistical parameter is or you’re foggy on how probability distributions work, I recommend scooting over to my beginner-friendly intro here in Part 1 before continuing here.

Mean

This word is pronounced “average.”

Expected value

An expected value, written as E(X) or E(X=x), is the theoretical probability-weighted mean of the random variable X.

You find it by weighting (multiplying) each potential value x that X can take by its corresponding probability P(X = x) and then combining them (with an integral for continuous variables like height or a sum for discrete variables like height-rounded-to-the-nearest-inch): E(X) = ∑ x P(X=x)

If we’re dealing with a fair six-sided die, X can take each value in {1, 2, 3, 4, 5, 6} with equal probability 1/6, so:

E(X) = (1)(1/6) + (2)(1/6) +(3)(1/6) +(4)(1/6) +(5)(1/6) +(6)(1/6) = 3.5

In other words, 3.5 is the probability-weighted average for X and nobody cares that 3.5 isn’t even an allowable outcome of the die roll.

Variance

For reasons that I’ll explain in a moment, replacing X with (X — E(X))² in the E(X) formula above gives you something very useful.

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Source: Medium