About this video
The video explains the difference between numerical data, which measures or counts a quantity, and categorical data, which sorts answers into groups. 'Which instrument does each student play?' gives categorical data. Bus numbers are also categorical, because the numbers are just labels and don't measure anything.
You'll be able to
- tell numerical data from categorical data.
- explain why numbers used as labels give categorical data.
- spot wrong reasons for calling data numerical or categorical.
Key words
- numerical data
- Data made of numbers that measure or count something, like hours of practice.
- categorical data
- Data that puts answers into groups or categories, like instrument names.
- label
- A name used to identify something; numbers can be labels, like a bus number.
Transcript
- "A music teacher asks, 'Which instrument does each student play?' What type of data set does this question produce?" Pause this video, have a go at that. Okay, so it looks like all the choices they're talking about whether it's the numerical data or categorical data.
And just so that you know the difference, numerical data is where, for example, if the teacher said, "How many hours do you practice your musical instrument?" And one student said, "Five," and the next student said, "Four," and the next student said "Six," then that would be numerical data.
But in a situation where we're saying, "Which instrument?" And one student's going to say, "The tuba," and one student's going to say, "Guitar." So this is categorical. We're putting things, the answers can be put into categories. So this first one, "The data set is numerical because we can count how many students play each instrument."
That's not the data that we are actually collecting. We want to know which instrument does each student play. If they, if the teacher had asked how many student, how many instruments you play, then it would have been numerical, but that's not what was being asked.
"The data is categorical," which is true, "Because there are many students in the same music program, in the music program." No, that's not the reason it's categorical. The reason it's categorical is because it describes, in this case, C, a quality or a characteristic.
I like that one. And then last, we know it's not numerical and it's not numerical for sure because the instruments can be assigned number codes. That, just that still puts it in categories. You aren't quantifying, it's not a qual-, in this situation, it is a quality or a characteristic.
We're not measuring how much of something, we're not quantifying something. So that's why we like choice C. Now, let's do another, let's do another example here. So let me bring up the next question. "A student records the bus number they take to school each day for a week." All right.
"What type of data is represented in this list?" Now pause the video, have a go at this. Okay, before I even look at the choices, it's tempting to think, "Well, I see a bunch of numbers here. Maybe this is numerical data." Numerical. Now, the key between categorical and numerical data isn't whether it's just words or numbers.
It's whether those numbers are actually quantifying or measuring something. In this situation, the numbers are really just the names of the bus. They're just, really, labels for these buses. You could even think of them as categories or labels of the buses. So even though there's numbers involved here, they're not actually measuring anything that we care about.
So this one is actually going to be categorical. Categorical. Where the numbers are just the categories or the names or the labels. So, "The data is categorical because the list has seven entries." No, that's not a reason to be categorical. "The data is numerical because the bus numbers can be ordered from least to greatest."
That is true that it can be ordered, but that doesn't make it numerical data. In order for that to be numerical, it has to be measuring or quantifying something that we actually, that we, something meaningful, something that we care about. "The data set is categorical because the bus numbers label groups."
Yep, that's exactly right. Another way to think about it, this would be no different, instead of naming this bus 42 and this one 15, we could've named this first one Alpha and the second one Bravo and so on and so forth. They didn't have, the numbers are just names.
"The data set is numerical because we can find the mean of the bus numbers." We can find the mean of the bus numbers, but that doesn't really mean anything. No pun intended. So, 'cause we're not, these aren't actual measurements. So once again, we would rule that out as well.
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