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The Variance: Measuring Dispersion

Posted on December 8, 2018 Written by The Cthaeh 2 Comments

Small pawn-shaped magnets of different color, representing varianceA few posts ago I introduced you to the “three M’s” of statistics — the concepts of mean, mode, and median. Today I want to talk to you about a related concept called variance.

While the three M’s measure the central tendency of a collection of numbers, the variance measures their dispersion. That is, it measures how different the numbers are from each other.

Measuring dispersion is another fundamental topic in statistics and probability theory. On the one hand, it tells you how much you can trust the central tendency measures as good representatives of the collection. High variance usually means a lot of the numbers in the collection will be far away from those measures.

[Read more…]

Filed Under: Fundamental Concepts, Measures Tagged With: Mean, Parameter estimation, Variance

Intuitive Explanation of Expected Value

Posted on November 24, 2018 Written by The Cthaeh 20 Comments

A pile of poker chips and a few dice

Expected value is another central concept in probability theory. It is a measure of the “long-term average” of a random variable (random process). I know this doesn’t sound too clear, but in this post I’m going to explain exactly what it means.

There are many areas in which expected value is applied and it’s difficult to give a comprehensive list. It is used in a variety of calculations by natural scientists, data scientists, statisticians, investors, economists, financial institutions, and professional gamblers, to name just a few.

[Read more…]

Filed Under: Fundamental Concepts, Measures Tagged With: Coin flip, Expected value, Law of large numbers, Mean

The Mean, the Mode, And the Median

Posted on October 1, 2018 Written by The Cthaeh 3 Comments

Mean, median, and mode of a distribution shown on a Spaghetti Western background

The concepts of mean, median, and mode are fundamental to statistics, probability theory, and anything related to data analysis as a whole. Being this important, they deserve their own introduction.

In statistics, these 3 concepts are examples of measures of central tendency. This is a fancy way of saying that they are single values that summarize collections of values.

Let’s unpack the last sentence. What exactly do I mean by ‘values’ and ‘collections of values’?

[Read more…]

Filed Under: Fundamental Concepts, Measures Tagged With: Mean, Parameter estimation

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