An explanation of the difference between discrete and continuous outcomes.
- As we dive a bit deeper into probabilities, we need to take note of different types of outcomes. We'll be looking at both discrete random variables and continuous random variables. Let's first break down the use of the term random variable. Why random? Why do we use that word? Well, as we perform experiments, we need to understand that the value of the eventual outcome of the experiment is unknown, or random. Thus, the result of the experiment is called a random variable.
So, trying to predict the number of drinks, the next customer, in line at Starbucks, will order is a random variable. The sum of dots on a single roll of two dice is a random variable. The amount of rain that will fall, in London this month is a random variable. The length of time you will wait in line at Starbucks tomorrow, that too is a random variable. But even among these examples, there are different types of random variables. The number of drinks, the next Starbucks customer will order, is very likely as low as zero, perhaps they just wanted a food item, but probably no larger than 10.
And since they can't order half drinks, the number has to be a whole number. This is an example of a discrete random variable. The same thing goes for the second example. The sum of dots on a single roll of two dice. The only possibilities are two through 12. Again, we do not have any decimals. This too would be a discrete probability. But our two other examples are different. These are continuous random variables.
Why? Well, in the case of rainfall, the amount of rainfall, in London for the month, might be 0.26 inches. It might be 1.35 inches. It might even be 2.77 inches. There really is no end to the possible rain outcomes for this month. The same goes for your wait at Starbucks tomorrow. You might wait 36 seconds, four minutes and 17 seconds, or perhaps they are very busy, and you end up waiting 10 minutes and 33 seconds.
Again, the possibilities are endless. So, why is this distinction between discrete and continuous important in determining probabilities? Let's start with our dice. A nice and predictable experiment. Probability tells us that the distribution of possible outcomes would look like this. How about the distribution of drinks ordered by each customer, at one store, during a two hour period? Perhaps it might look something like this.
There are a limited number of possible outcomes and because of this, the distribution tables are very helpful. On the other hand, let's look at a possible distribution of rainfall in London for the last 20 months of October. The same number doesn't even come up once. Here's what the bar chart would look like. We sort of see the same thing with a list of the wait times for the 25 customers that came to our Starbucks in a single hour. Here's the bar chart for this.
Since we have an endless number of possibilities for the continuous random variables, we need to consider alternative ways to calculate those types of probabilities. So, before we delve into discrete and continuous random variable probabilities, look around you. Consider your place of work. Think of your favorite sports. Think about environmental data. Can you identify discrete random variables and continuous random variables, in your life, in the world around you? And as you do that, start to think about how probabilities are calculated and discussed differently in each scenario.
Professor Eddie Davila covers statistics basics, like calculating averages, medians, modes, and standard deviations. He shows how to use probability and distribution curves to inform decisions, and how to detect false positives and misleading data. Each concept is covered in simple language, with detailed examples that show how statistics are used in real-world scenarios from the worlds of business, sports, education, entertainment, and more. These techniques will help you understand your data, prove theories, and save time, money, and other valuable resources—all by understanding the numbers.
- Calculate mean and median for specific data sets.
- Explain how the mode is used to assess a data set.
- Identify situations in which standard deviation can be used to investigate individual data points.
- Use mean and standard deviation to find the Z-score for a data point.
- List the three different categories of probability.
- Analyze data to determine if two events are dependent or independent.
- Predict possible outcomes for a situation using basic permutation calculations.
- Give examples of binomial random variables.