Types of Data in Statistics

Parameter vs. Statistic

• Parameter: Numerical measurement describing a characteristic of a population.
  • Example: Mean height of a population, total number of M&Ms in a pack.
• Statistic: Numerical measurement describing a characteristic of a sample from a population.
  • Example: Average height from a sample group, number of M&Ms in a sample pack.

Types of Data

Quantitative Data

• Consists of numbers representing counts or measurements.
• Can be discrete or continuous.
  • Discrete Data:
    • Countable, finite numbers.
    • Example: Sum of values from dice rolls (2 through 12).
  • Continuous Data:
    • Can take any value within a range.
    • Example: Milk production in liters (2.37 liters).

Qualitative Data

• Also known as categorical or attribute data.
• Consists of names or labels (non-numeric).
• Examples: Political affiliations, types of fruit.

Levels of Measurement

1. Nominal Level

   • Data consists of names, labels, or categories.
   • No meaningful order.
   • Example: Political party affiliations.

2. Ordinal Level

   • Data can be organized in a meaningful order.
   • Differences between data are not meaningful.
   • Example: Grades (A, B, C), can be ordered but not subtracted meaningfully.

3. Interval Level

   • Differences between data are meaningful.
   • No natural zero starting point.
   • Example: Years of birth (calculate age difference, but year zero is arbitrary).

4. Ratio Level

   • Differences are meaningful, with a natural zero starting point.
   • Example: Amount paid for gas (0 dollars if buying 0 gallons).

Key Concepts

• Natural Zero: A point where zero means none is present (e.g., zero gallons of gas).
• Meaningful Differences: Ability to compare differences meaningfully.

Practice Exercise

• Match terms with definitions to reinforce understanding of concepts. Answers provided for self-assessment.