Unit 1 · Topic 1.2 Beta

Variables

Observational units are the individuals in a data set, and variables are the characteristics recorded for each.

Practice 2: Collect Data

Part 1 · Hook

Why this matters

An animal shelter keeps a record for every dog: its size group, whether it is vaccinated, its kennel number, how many times it has been adopted, its weight. Before you can summarize any of it, you have to know what kind of information each column holds. A kennel number is a number, but its average tells you nothing. Sorting the columns is the first job of every analysis.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. A city asks 500 of its 80,000 adults about a new park. What is the sample?

  1. The 500 adults who were asked
  2. The 80,000 adults in the city
  3. The new park
  4. The city council
Show the answer

The sample is the part of the population that data come from.

  • Correct: The 500 adults who were asked:
  • The 80,000 adults in the city:
  • The new park:
  • The city council:

2. Which question needs data from many individuals?

  1. How long do adults in the city spend commuting?
  2. How long is the main bridge?
  3. What year was the park built?
  4. How many members are on the city council?
Show the answer

Commute times vary from person to person; the other answers are single facts.

  • Correct: How long do adults in the city spend commuting?:
  • How long is the main bridge?:
  • What year was the park built?:
  • How many members are on the city council?:

Part 4 · See it

See it first

A data table about shelter dogs with columns Dog, Size group, Vaccinated?, Times adopted and Weight in kilograms, and four dogs as rows. Size group and Vaccinated? are tagged categorical. Times adopted is tagged quantitative, discrete. Weight is tagged quantitative, continuous. One row is outlined and labeled: a row is one observational unit, one dog. The weight column is outlined and labeled: a column is one variable, a characteristic recorded for every dog.
In a data table each row is one observational unit and each column is one variable. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Each row of a data table is one individualthe individuals are the observational units
  2. Each column records one characteristic for every individualeach column is a variable, and its values can differ from row to row
  3. Some variables put individuals into groups, others record amountscategorical and quantitative variables need different summaries and graphs
  4. A number can describe the whole population or only the sampleit is a parameter (usually unknown) or a statistic (used to estimate the parameter)

Part 6 · Key ideas

Key ideas

  • An observational unit is one individual the data describe: a person, a dog, a fish, a day. A variable is a characteristic recorded for each unit.
  • A categorical variable places each unit in a group (size group, yes or no). A quantitative variable records an amount, where arithmetic makes sense.
  • Quantitative variables are discrete (separate values, usually counts) or continuous (any value in an interval, usually measurements).
  • Numbers that are labels, such as ZIP codes or jersey numbers, are categorical.
  • A parameter describes a population; a statistic describes a sample. The distribution of a variable tells what values it takes and how often.

Part 7 · Misconception

A common mistake

The wrong idea: Kennel number is quantitative, because its values are numbers.

What actually happens: Kennel numbers are labels. Ask whether arithmetic makes sense: an average kennel number tells you nothing, so the variable is categorical.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Table

Records for five shelter dogs

An animal shelter keeps one record for each dog in its care. Part of the table is below (invented data).
Shelter records
DogSize groupVaccinated?Kennel numberTimes adopted beforeWeight (kg)
Milosmallyes1406.8
Nalalargeno3129.4
Otismediumyes22215.1
Pipsmallyes704.9
Rosielargeyes18133.0

1. What are the observational units in this table?

  1. Kennels
  2. The dogs
  3. The size groups small, medium and large
  4. The columns of the table, one for each characteristic
Show the answer

Each row describes one dog, so the dogs are the observational units.

  • Kennels: Kennel number is one of the variables recorded about each dog; the rows are dogs.
  • Correct: The dogs: Right: each row is one dog, and every variable is recorded for each dog.
  • The size groups small, medium and large: Those are values of one variable, size group.
  • The columns of the table, one for each characteristic: Columns are variables. Observational units are what each row describes.

2. Which variable is categorical even though its values are numbers?

  1. Weight (kg)
  2. Times adopted before, a count for each dog
  3. Vaccinated?, recorded as a yes or a no
  4. Kennel number
Show the answer

Kennel numbers name places; doing arithmetic with them makes no sense, so the variable is categorical.

  • Weight (kg): Weight is a measured amount, so it is quantitative.
  • Times adopted before, a count for each dog: A count is quantitative: 2 adoptions is twice as many as 1.
  • Vaccinated?, recorded as a yes or a no: This is categorical, but its values are words, not numbers.
  • Correct: Kennel number: Right: a kennel number is a label. Averaging two kennel numbers gives nothing useful.

3. How should "Times adopted before" be classified?

  1. Quantitative and discrete
  2. Quantitative and continuous, like any measurement
  3. Categorical, because it takes just a few different values
  4. Categorical
Show the answer

A count is quantitative, and since it takes whole-number values with gaps between them, it is discrete.

  • Correct: Quantitative and discrete: Right: it is a count, and counts take separate whole-number values.
  • Quantitative and continuous, like any measurement: A count jumps from 0 to 1 to 2; it does not take every value in between.
  • Categorical, because it takes just a few different values: Having few values does not make a variable categorical; these values are amounts.
  • Categorical: Every variable is recorded for each dog. What matters is whether the values are amounts.

4. Which variable is quantitative and continuous?

  1. Times adopted before, which takes the values 0, 1 and 2
  2. Kennel number, which runs from 1 up to about 25
  3. Weight (kg)
  4. Size group
Show the answer

A continuous variable is measured and can take any value in an interval. Weight is one.

  • Times adopted before, which takes the values 0, 1 and 2: A count is discrete: no dog has been adopted 1.5 times.
  • Kennel number, which runs from 1 up to about 25: Kennel numbers are labels, so the variable is categorical.
  • Correct: Weight (kg): Right: weight is measured and can take any value in a range, such as 15.1 or 15.13 kg.
  • Size group: Size group puts dogs into groups, so it is categorical even though the groups have an order.

Table

Seniors with part-time jobs

District records show that 31% of the 1,250 seniors in a school district have a part-time job. A reporter chooses 80 of the district’s seniors at random and finds that 26% of the 80 have a part-time job. Those with jobs work an average of 14 hours a week (invented data).

5. In this situation, what is the 31%?

  1. A statistic, because it is written as a percent
  2. A variable
  3. A parameter
  4. An observational unit of the reporter’s study
Show the answer

A parameter is a number that describes a population. The 31% describes all 1,250 seniors.

  • A statistic, because it is written as a percent: A statistic describes a sample. The 31% comes from records on every senior.
  • A variable: A variable is a characteristic of each senior, such as whether that senior has a job.
  • Correct: A parameter: Right: 31% describes the whole population, all 1,250 seniors in the district.
  • An observational unit of the reporter’s study: Observational units are the seniors themselves, not a number about them.

6. In this situation, what is the 26%?

  1. A statistic
  2. A parameter, because it describes the district’s seniors
  3. A variable
  4. The population that the reporter wants to learn about
Show the answer

A statistic is a number that describes a sample. The 26% describes the 80 seniors chosen.

  • Correct: A statistic: Right: 26% describes the sample of 80 seniors the reporter asked.
  • A parameter, because it describes the district’s seniors: It describes only the 80 seniors in the sample, so it is a statistic.
  • A variable: "Has a job" is the variable; 26% is a number that summarizes it for the sample.
  • The population that the reporter wants to learn about: The population is the 1,250 seniors; 26% is a number found from the sample.

7. A league’s official roster lists every player. From it, the average height of all players in the league is 191 cm. A fan measures 12 players and finds an average of 189 cm. Which is correct?

  1. 191 cm is a statistic and 189 cm is a parameter
  2. Both are statistics, because both are averages of heights
  3. Both are parameters, because both describe league players
  4. 191 cm is a parameter and 189 cm is a statistic
Show the answer

A parameter describes a population (the whole league); a statistic describes a sample (the 12 players).

  • 191 cm is a statistic and 189 cm is a parameter: This reverses them: the roster covers the whole league, the population.
  • Both are statistics, because both are averages of heights: Whether a number is a parameter or a statistic depends on the group it describes, not on how it is computed.
  • Both are parameters, because both describe league players: The 189 describes only the 12 measured players, a sample.
  • Correct: 191 cm is a parameter and 189 cm is a statistic: Right: 191 describes every player in the league; 189 describes the 12 measured.

Part 9 · Summary

Summary

Observational units are the individuals in a data set, and variables are the characteristics recorded for each. Categorical variables sort units into groups; quantitative ones record amounts, discrete or continuous. A parameter describes a population, a statistic describes a sample, and a distribution tells what values a variable takes and how often.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections

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