![]() ![]() Without wasting any more time, you pack your bags and catch the first space ship. Perfect, that’s exactly what you were looking for. You read that the average temperature there is 25° Celsius. Then you hear about this newly discovered planet called Discordia. You’ve also heard that the average temperature on Venus is around 450° Celsius and you certainly don’t want to go there either! You’ve heard, for example, that the average temperature on Saturn is around -180° Celsius. The only important thing for you is that the typical temperature on the new planet shouldn’t be anything crazy. You’re kind of an adventurous person and you don’t have too many capricious demands regarding where you want to live next. You’re bored of living on Earth and decide to take off towards another planet. We’ve started colonizing and populating new planets. Imagine our technology has advanced so much that we can freely travel in space. Let’s start with a funny (and not so realistic) example. The mathematical definition of variance.Also, to see two very useful alternative representations of the variance formula, check out my post showing their derivation and intuition. ![]() ![]() To see how that generalizes to probability distributions, check out my post on calculating the mean and variance of a probability distribution. This post is about measures of dispersion of finite collection of values. To get the big picture, I’m also going to show a few alternative measures of dispersion. In the following sections, I’m going to show the mathematical definition of variance with a few examples to give you an intuitive feel for it. It’s a central part of many tools and techniques in descriptive and inferential statistics, machine learning, data engineering, and so on. High variance usually means a lot of the numbers in the collection will be far away from those measures.īut the importance of variance is far greater. On the one hand, it tells you how much you can trust the central tendency measures as good representatives of the collection. Measuring dispersion is another fundamental topic in statistics and probability theory. That is, it measures how different the numbers are from each other. While the three M’s measure the central tendency of a collection of numbers, the variance measures their dispersion. Today I want to talk to you about a related concept called variance. A few posts ago I introduced you to the “three M’s” of statistics - the concepts of mean, mode, and median. ![]()
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