# Probability and Statistics

### Topics

## Introduction to :

One other type of data you'll need to know is **categorical** data. This is data that can be organized into mutually exclusive categories. If we look at a bunch of bananas and they're all either green, brown, yellow or blue, then we could use the categories "green," "brown," "yellow" and "blue" to record our data. We'd stay away from the blue ones if we were you.

### A Few Examples

**Four students had brown hair, six had blonde hair, and three had red hair.**

This statement refers to categorical data. The categories are the different colors of hair that have been observed: brown, blonde, and red. Incidentally, most of the blonde students got this question wrong.

**The car is orange-red.**

This statement sounds like it's referring to categorical data, but it isn't. This statement refers to data that is qualitative, but not categorical. There isn't enough information to determine what the categories would be. If we went with the standard colors of the rainbow, to what category would the color "orange-red'' belong? We don't remember there being an "orange-red" Wiggle.

Categorical data is usually qualitative. However, quantitative data can also be put into categoriesâ€”more on this later.

### Sample Problem

There's a family in which the dad is 5'11'', the mom is 5'7'', and the kid is 4'8''. The mom is a little unnerved by how quickly her daughter is gaining on her, but it's irrelevant to this problem, so don't let it bother you.

Anyway, these are measurements, and are therefore quantitative data. However, we could also say that both the dad and the mom are between 5 and 6 feet tall, and the kid is between 4 and 5 feet tall. If we say this, we've taken our quantitative data and put it into categories. The categories are "5 to 6 feet tall," "4 to 5 feet tall," and so on. If the dog wants to play, we'll need to add a "1 to 2 feet tall" category.

To summarize what we have so far, data is either quantitative (about quantities or numbers), or qualitative (about non-measurable qualities). Sometimes data can be turned into categorical data by putting it into categories. Or by waving a wand over it and saying "categoriarmus!"

Most of our statistics will be done on quantitative data, since this is math, after all. We can also do some things with categorical data. It's hard to analyze data that's qualitative and not categorical, since we need to have numbers somewhere. Yes, we're a slave to numbers. We're seeing someone about it.

#### Exercise 1

Determine whether the following statement refers to categorical data, qualitative data, quantitative data, or some combination of these:

Mrs. Smith gave a test on which the maximum possible score was 100. The actual scores students received were 92, 87, 86, 85, 72, 70, 70, and 61.

#### Exercise 2

Determine whether the following statement refers to categorical data, qualitative data, quantitative data, or some combination of these:

Mrs. Smith gave an exam on which one student received an A, three students received B's, three students received C's, and one student received a D.

#### Exercise 3

Determine whether the following statement refers to categorical data, qualitative data, quantitative data, or some combination of these:

Mr. Lee ran 63 km last week.

#### Exercise 4

Five students had blue backpacks, ten students had red backpacks, and three students had green backpacks.

#### Exercise 5

Luisa's hair is reddish-blonde.