One of my pet peeves (I have many!) is when I hear a sports announcer speak of the “amount of runs” that have been scored in this game. “Less commercials” used in a television network ad makes me want to scream. What they should have said was “number of runs” and “fewer commercials” since runs scored and television commercials are measured in whole numbers only. There’s no such thing as half of one…
As much as this annoys me, it is just bad grammar. The user’s point is still communicated to me. However, when it comes to plotting and analyzing data, knowing the difference between “whole number only” and “infinitely divisible” measurements is critical. Critical! Choosing a tool to analyze and/or graphically represent data depends upon what type of data it is. The wrong tool can yield wrong conclusions.
This post will not go into which type of data is better or why; we’ll save that for next time. For now, let’s define the two types of data that matter when using most statistical analysis and graphical tools: Discrete and Continuous.
No, not discrete as in “can keep a secret”. In this case, discrete refers to all measurements that don’t make sense in smaller portions. You can’t divide the measurement in half - or by any amount - and have something that means anything in the physical world.
- Runs in a baseball game
- Points in any sporting event
- Automobiles built, sold, registered, on the road…
- Students taking a Moodle course
- Seats on a train
- Bottles of wine, if you are measuring the containers, not the liquid inside
- Number of times you’ve started the engine on your car
- Words in your latest book
- Typographical errors in your latest book
Of course, you can have an average of 3.1 points in a game, which makes sense if you know how to use and interpret averages. We’ll get into that soon, in a discussion of the Central Limit Theorem. For now, let’s stick to the actual measurements, not their averages.
If you have five bottles of wine, using proper grammar, you would refer to the number of bottles. The number of bottles is a discrete measurement. Inside those bottles (assuming you didn’t drink it yet) would be an amount of wine. The volume of liquid is a continuous measurement.
This type of data is measured in a way that is infinitely divisible. Whether you want to or not, you can measure the amount of wine in units as small as a centiliter, a micro liter… or even smaller still.
There are some categories of data measurements that are always continuous, regardless of what units we typically use:
- Money (wealth, not currency, which is discrete)
This is where math and grammar diverge. Even though it would be proper grammar to say “the number of pounds”, any measurement of weight, regardless of the units, would be continuous data. Examples of continuous data, no matter how you say it in English:
- Liters of wine, number of liters, volume of wine, amount of wine
- Kegs of beer, bottles of beer, glasses of beer…IF you are measuring the amount of beer (not the containers)
- Miles (or kilometers) to Grandmother’s house
- Age of your car (or anything), in years, months, days, millennia…
- Ink (or paper) used in the production of your latest book
Understanding the difference between discrete and continuous (sometimes called variables) data is foundational to using tools to compile, analyze, and graphically display data. When you’re stuck in commuter traffic or alone with your thoughts, quiz yourself on the difference until it becomes second-nature!
If you want to hone your grammatical skills, this is a great site: Grammar Girl.
For more on this topic, consider taking the Data 101 course at BeeLearn.com.