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​Random Variables - Do You Know What They Are?

Random Variables might not seem like a lot of fun - especially at parties - but if you ever need to analyse data, then you'll need to know what they are and what you can do with them.

To be honest, it's all pretty simple and there's not a lot to learn, but getting the basics right can mean the difference between your analyses being correct or completely and utterly wrong.

​For a while now I've been researching all the little nooks and crannies of the statistics world to create a big picture of what it looks like when you pull it all together.

And this is what the part about ​Random Variables looks like:

Random Variables - Do You Know What They Are?

Choices, Choices...

And now I'm going to give you a choice...

Ooh, I like choices!

You can either watch the video below to learn more about ​random variables or you can read the text instead.

It's up to you...

Introduction to ​Random Variables

Here, I'm going to give you an introduction to ​random variables and you'll learn that there are only 2 types​​:

  1. 1
    ​Discrete random variables
  2. 2
    ​Continuous random variables

And just so you know, this video lesson is actually one of the lessons in The Hive from our exclusive video course Statistics - The Big Picture, which is Open Access to start with (you don't need to register).

If you want to continue learning, you can start from the beginning here:

1. ​Discrete Random Variables

​Discrete random variables are better known as ​Categorical variables, and have the following properties

  • ​They are observed
  • ​They can only take distinct values
  • ​Their values are finite

Discrete random variables are observed and can often be described as having qualities that are difficult (or impossible) to measure or define mathematically, and as such are arranged in categories.

They can only take distinct values, meaning that categories are distinct from each other.

Discrete random variables can only take finite values, so that categories cannot be subdivided.

Introduction to Random Variables

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​An example of a discrete random variable is Gender.

Gender cannot be measured, it can only be observed, there are distinct categories, male and female, and categories cannot be subdivided - there aren't "degrees of maleness" or "degrees of femaleness".

Similarly, T-shirt sizes are observed (there is no single measurement), distinct (sizes can be Small, Medium or Large), and finite (there is no size category of "Small-and-a-bit").

2. ​Continuous Random Variables

On the other hand, continuous random variables have the following properties:

  • ​They are ​measured
  • ​They can ​take ​interval values
  • ​Their values are infinite

​Continuous random variables are measured ​with some kind of measuring implement, such as a ruler, a stopwatch or a jug, and these measurements can take any value such as 1.23 or 15.78.

More importantly, inbetween each measurement there can exist an infinite number of values

Random Variables​​ - Do You Know What They Are?​ (video) #​statistics @chi2innovations @eelrekab

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​An example of a continuous random variable is ​Distance.

​Distance is measured with a ruler (or something similar) and can take any value​ - the distance between a pair of electrons in an atom ​is quite small, whereas the distance between galaxies is somewhat larger. The distance between measurements can be subdivided, so metres can be divided into centimetres, millimetres, nanometres, and so on.

​Random Variables - A Summary

​So the bottom line here is that there are 2 types of random variable - discrete random variables and continuous random variables.

Discrete variables are basically those that cannot be easily measured, but are instead observed and placed into categories - they are qualitative data.

Continuous variables are those that can be measured and can take any value - they are quantitative data.

I appreciate that ​Random Variables aren't the sexiest things on the planet, so if you've got this far without running away, well done!

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Statistics - The Big Picture

I hope you enjoyed this video lesson.

It's actually one of the lessons in The Hive from our exclusive video course Statistics - The Big Picture, where I take you through all the nooks and crannies of the statistics world.

This course is Open Access to start with (you don't need to register), and after you've gone so far through you'll need a Free Plan to continue.

As part of the course you'll get an Ultra-HD pdf of Statistics - The Big Picture to download and keep, and I'll share with you where you can also get your own poster to pin on your wall.

If you want to continue learning, you can start from the beginning here:

I look forward to seeing you on the inside!

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