Data Types

In this section, we will exploring the types, categorization, and the representation of the data.

In the context of statistics and data analysis, data types refer to the nature or characteristics of the values that a variable can take. There are two main types of data:

1. Categorical: Groups (e.g. brands, gender, yes/no)

2. Numeric: Numbers (Discrete (finite) and Continuous(infinite))

   1. Discrete Data: Discrete data consists of whole, distinct values, typically counting numbers. Examples include:

      • Number of customers in a coffee shop

      • Number of students in a class

      • Number of cars in a parking lot

   2. Continuous Data: Continuous data is characterized by an infinite number of possible values within a given range and often involves measurements. Unlike discrete data, fractional values are meaningful and can represent any point along a continuum. Examples include:

      • Height of individuals

      • Weight of an object

      • Temperature in degrees Celsius

There are also two ways to categorize the data:

• Based on Types of Data

  • Categorical

  • Numerical

• Based on Level of Measurement

  • Qualitative (Nominal and Ordinal) -> Related to Categorical Data

  • Quantitative (Interval (No True Zero) and Ratio (True Zero)) -> Related to Numeric Data

Let's explore data types based on Level of Measurements.

1. Qualitative Data (Categorical)

a. Nominal Data:

Nominal data represents categories with no inherent order or ranking. Examples include:

• Colors (e.g. red, orange, yellow, green, blue, indigo, violet)

• Gender (e.g. male, female)

• Marital Status (e.g. single, married)

• Car makes (e.g. toyota, honda, ford, tesla)

• Zipcodes ( e.g. 10001, 94074)

b. Ordinal Data:

Ordinal data signifies categories with a meaningful order, but the differences between them are not consistent or measurable. Examples include:

• Education levels (e.g., high school, bachelor's, master's)

• Customer satisfaction ratings (e.g., poor, satisfactory, excellent)

• Contractual membership levels (e.g. basic, pro, elite)

2. Quantitative Data (Numeric)

a. Ratio Data:

In ratio data, there is a true zero point, and ratios are meaningful. This means you can say that one value is "twice" or "three times" another. Examples include

• Weight of an object

• Income

• Annual sales

• Market share

b. Interval Data:

In interval data, there is no true zero point, and while differences between values are meaningful, ratios are not. For instance, a value of zero degrees Celsius or Fahrenheit does not signify the absence of temperature.

• Temperature in degrees Celsius or Fahrenheit

• SAT score (200-800)

• Credit score (300-850)

Representation of Data

Common tools/ways to represent

• Categorical Data:

  • Frequency Distribution Tables

  • Bar Charts

  • Pie Charts

  • Pareto Diagrams (Bar Chart + Cumulative Distribution Curve)

  • Cross (Contingency) Tables (for 2 Variables)

• Numeric Data:

  • Histograms

  • Scatter Plots (for 2 Variables)