Data Types, Sampling, and Quantitative vs Qualitative Data

Learning Objectives

• Data Types: Identify and distinguish between different types of data, including qualitative (categorical) data and quantitative data (discrete and continuous).

• Sampling Application: Apply various types of sampling methods to data collection.

Data Representation and Categorization

• Data Sources: Data may originate from a full population or from a representative sample.

• Variables and Values: Lowercase letters like $x$ or $y$ are generally used to represent data values.

• Primary Classifications: Most data can be categorized into two main divisions:

  • Qualitative data

  • Quantitative data

Qualitative Data

• Definition: Qualitative data are the result of categorizing or describing attributes of a population.

• Alternative Terminology: Qualitative data are also commonly referred to as categorical data.

• Descriptive Format: Qualitative data are generally described using words or letters.

• Examples of Qualitative Data:

  • Hair color (e.g., black, dark brown, light brown, blonde, gray, red)

  • Blood type (e.g., $A$, $B$, $O$, $AB$)

  • Ethnic group

  • The car a person drives

  • The street a person lives on

• Mathematical Limitations:

  • Researchers frequently prefer quantitative data over qualitative data because quantitative data lends itself more easily to mathematical analysis.

  • Calculating mathematical statistics for qualitative data is not meaningful; for instance, it does not make sense to calculate an average hair color or an average blood type.

Quantitative Data

• Definition: Quantitative data are always numbers and represent the result of counting or measuring attributes of a population.

• Examples of Quantitative Data:

  • Amount of money

  • Pulse rate

  • Weight

  • Number of people living in a town

  • Number of students who take statistics

• Subcategories: Quantitative data can be classified as either discrete or continuous.

Quantitative Discrete vs. Quantitative Continuous Data

• Quantitative Discrete Data:

  • Definition: All data that are the result of counting are defined as quantitative discrete data.

  • Numerical Values: Discrete data take on only certain specific numerical values (often whole counting numbers).

  • Daily Call Example: Counting the number of phone calls received on each day of the week produces discrete values such as $0$, $1$, $2$, or $3$.

  • Backpack Books Example:

  • Data Subject: The number of books students carry in their backpacks.

  • Sample: A sample of $5$ students.

  • Observed Data: Two students carry $3$ books, one student carries $4$ books, one student carries $2$ books, and one student carries $1$ book.

  • Classification: The counts of books ($3$, $4$, $2$, and $1$) are quantitative discrete data.

• Quantitative Continuous Data:

  • Definition: Data that are not limited to counting numbers, but may include fractions, decimals, or irrational numbers, are defined as quantitative continuous data.

  • Measurement Origin: Continuous data are typically the results of measurements, such as lengths, weights, or durations of time.

  • Call Duration Example: A list of the lengths in minutes for all phone calls made in a week, featuring values like $2.4$\,\text{minutes}, $7.5$\,\text{minutes}, or $11.0$\,\text{minutes}, constitutes quantitative continuous data.

  • Backpack Weight Example:

  • Data Subject: The measured weights of backpacks containing books.

  • Sample: The same sample of $5$ students.

  • Observed Data: Backpack weights (in pounds) are $6.2$\,\text{lbs}, $7$\,\text{lbs}, $6.8$\,\text{lbs}, $9.1$\,\text{lbs}, and $4.3$\,\text{lbs}.

  • Key Distinction: Backpacks containing the exact same discrete number of books (such as $3$ books) can yield different continuous weight measurements. Weights are quantitative continuous data.

Data Classification Examples

• Identification Rule: Data descriptions that are discrete often begin with the phrase "the number of."

• Classified Scenarios:

  • The number of pairs of shoes owned: Quantitative discrete data (result of counting).

  • The type of car driven: Qualitative / Categorical data (described by attributes or words).

  • The distance from home to the nearest grocery store: Quantitative continuous data (result of measuring continuous distance).

  • The number of classes taken per school year: Quantitative discrete data (result of counting whole units).

  • The type of calculator used: Qualitative / Categorical data (described by brand or model attributes).

  • Weights of sumo wrestlers: Quantitative continuous data (result of continuous physical measurement).

  • Number of correct answers on a quiz: Quantitative discrete data (result of counting correct responses).

  • IQ scores: Quantitative continuous data (measured on a continuous intelligence scale, though often debated).