Cases and variables: categorical and quantitative

About this lesson

Grade 6 › Data sets and distributions

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Cases and variables: categorical and quantitative

Discover

A spreadsheet has one row per student and columns for age, favorite color and number of pets. Which column holds categorical data?

  1. Favorite color
  2. Number of pets

Key idea

Data are values of variables recorded on cases.

Cases (individuals) are what the data describe; variables are what is recorded. A categorical variable places cases in groups; a quantitative variable takes numerical values for which arithmetic makes sense (discrete counts or continuous measurements).

Worked example

A café records each order: drink size (S, M, L), price in dollars, and table number.

Cases: the orders
Each row is an order.
Price: quantitative
Price: averaging makes sense.
Size and table number: categorical
Table numbers are labels; size is a category.

Your turn, guided

Your turn: how many quantitative variables among height, jersey number, goals scored?

22
Height and goals; jersey numbers are labels.

Practice ★

  1. A survey of 23 students records the following. Tick all the categorical variables.
    1. Eye color
    2. ZIP code
    3. Takes the bus to school (yes/no)
    4. Height in cm
    5. Number of siblings
  2. A survey of 80 students records the following. Tick all the categorical variables.
    1. Eye color
    2. ZIP code
    3. Takes the bus to school (yes/no)
    4. Height in cm
    5. Number of siblings

Watch out!

Practice ★★

  1. Area codes such as 770 are numbers. Is the area code of a phone number a quantitative variable?
    1. No: it is categorical, a label that only looks like a number
    2. Yes: its values are numbers
    3. Yes, a discrete quantitative variable
  1. A study measures the resting heart rate of 29 runners. What are the cases (observational units)?
    1. The 29 runners
    2. The heart rates
    3. The number 29

Exit ticket

Three questions to check you have got it.

  1. A survey of 23 students records the following. Tick all the categorical variables.
    1. Eye color
    2. ZIP code
    3. Takes the bus to school (yes/no)
    4. Height in cm
    5. Number of siblings
  2. A survey of 80 students records the following. Tick all the categorical variables.
    1. Eye color
    2. ZIP code
    3. Takes the bus to school (yes/no)
    4. Height in cm
    5. Number of siblings
  3. A survey of 54 students records the following. Tick all the categorical variables.
    1. Eye color
    2. ZIP code
    3. Takes the bus to school (yes/no)
    4. Height in cm
    5. Number of siblings

Summary card

Variables

  • Cases: who or what. Variables: what is recorded.
  • Categorical: groups. Quantitative: meaningful numbers.

Watch out: numeric codes (ZIP, ID) are categorical.

End of the lesson

Next lesson: Displaying and describing distributions Back to the chapter

Answers: Cases and variables: categorical and quantitative

A

  1. Eye color · ZIP code · Takes the bus to school (yes/no)
  2. Eye color · ZIP code · Takes the bus to school (yes/no)

B

  1. No: it is categorical, a label that only looks like a number

C

  1. The 29 runners

D

  1. Eye color · ZIP code · Takes the bus to school (yes/no)
  2. Eye color · ZIP code · Takes the bus to school (yes/no)
  3. Eye color · ZIP code · Takes the bus to school (yes/no)

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