What is the meaning of discrete and continuous data?
In: Mathematics
Discrete data is like counting whole things, like how many cookies you have. Continuous data is like measuring something that can be any value, like how tall you are.
Continuous data is data that is data that exists on a scale. So if you were measuring the height of everyone in a group, the data you produce would be continuous data.
Discrete data is data that isn’t on a scale like that. So if you were counting in that group how many people had blue eyes and how many people had brown eyes, that would be discrete data.
Discrete
Whole numbers like 2,4,16,196, etc.
Continuous
Starting from 0 to infinity with everything in between. 0.1, 0.2, 0.3, and on and on.
Continuous data is where there are infinite measurements over any time period. So it’s like measuring a temperature with a thermometer, and you watch it constantly change.
It becomes discrete data when your mate asks you what the temperature is, and you read out what you see. Each time you read it out is you sampling the value.
If you spoke faster, then you could read out the value more often and, in other words, sample more often. If you could speak infinitely fast and read out the values infinitely often, then it becomes continuous data.
But since we can’t do things infinitely fast, discrete data is how continuous data can be represented in a digital world.
Discrete data is data sampled in some time interval, continuous data is data that is sampled… well… continuously.
A good way to think about it is a [seismograph](https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Kinemetrics_seismograph.jpg/640px-Kinemetrics_seismograph.jpg). It has an “infinite” piece of paper that is rolling under the needle at all times, so it draws an “infinite” line (it plots continuous data).
Now imagine that instead of rolling piece of paper we had a camera taking pictures of the needle, at a frequency of 1000 pictures per second, and each time a picture is taken, a dot is added in the paper signaling the place where the needle was (it would plot discrete data).
If you zoom out they both look the same but if you zoom in a lot to see where was the needle at exactly 8 hours, 8 minutes, 8 seconds and 0.0008 milliseconds, you would see the line in the continuous data but you would find a dot at 0.000 milliseconds, another dot at 0.001 milliseconds and nothing in between, so you can’t tell where the needle was at 0.0008.
Imagine the data is a rope. Continuous is a like the whole rope, discrete would be chopping the rope with a knife into separate *discrete* parts of subrope. Its not continuous.
Picture a Sine wave, draw it on a graph. Along the length of the Sine wave, put 10 equally spaced tick marks on the axis. At each tick mark, put a dot on the Sine wave. Continuous data is the Sine wave you drew with an infinite amount of points. Now if you erase the line you drew and leave the dots and connect them with straight lines, that is discretely sampled data.
You can think of continuous data as all the possible points on a line or curve.
Discrete data are a a collection of points that are not connected to each other. Sometimes discrete data can be used to approximate continuous date. For example age, measured in years can be fit to a regression model and we consider it continuous over its range. Discrete data can also be ordinal or nominal, while continuous data cannot.
Ordinal data has order, but the interval between points is not consistent. For example, a five-point rating scale is ordinal. We know that a rating of ⭐️⭐️⭐️⭐️⭐️ is better than ⭐️⭐️⭐️⭐️ but that one star difference may not represent the same amount of change in quality than the difference between ⭐️⭐️⭐️ and ⭐️⭐️.
Discrete data may also be nominal, I.e., unordered or categorical. Gender, color, or really any characteristic that is not numeric fits into this category.
I have a TV. When I push volume up it goes up by 1, from 7 to 8. That is discrete.
I also have a very old radio that has a know and doesn’t hlknow settings like 7 or 8 or how to go up by 1. I turn it and the volume goes up or down by the amount I turn.
The latter is analog. There are infinitely many settings I can dial in.
Discrete data means there are breaks between possible values
Yes or no, true or false answers are discrete
The integers are discrete numbers
Note, this is different from discreet, which means secret.
Continuous data means there aren’t breaks between possible values. Ie the real numbers.
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