Introduction to Statistics: Types of Data

Parameter vs Statistic

• Parameter: A numerical measurement describing a characteristic of a population.
  • Example: Median home value of an entire city’s records is $200,000 (parameter).
• Statistic: A numerical measurement describing a characteristic of a sample.
  • Example: 40% of a sample of 500 gym members are satisfied (statistic).
• Memory Aid: Parameter is for population; statistic is for sample.

Types of Data

1. Quantitative Data

• Represents counts or measurements.
• Examples: IQ, height, energy usage.
• Divided into:
  • Discrete Data: Can take on only certain values.
    • Finite: Limited number of values (e.g., number of patients seen by a doctor).
    • Countable: Infinite but countable values with a natural next (e.g., number of coin tosses).
  • Continuous Data: Can take any value within a range.
    • Example: Length measurements; thermometer readings (mercury).

2. Categorical/Qualitative Data

• Consists of names or labels.
• Examples: Eye color, gender, city of residence.

Levels of Measurement

1. Nominal Level

   • Data cannot be ordered.
   • Examples: Eye color, survey responses like yes/no.

2. Ordinal Level

   • Data can be ordered, but differences are meaningless.
   • Examples: College rankings, course letter grades.

3. Interval Level

   • Data can be ordered, and differences are meaningful.
   • No natural zero starting point.
   • Examples: Years, body temperature.

4. Ratio Level

   • Data can be ordered, differences are meaningful, and there is a natural zero.
   • Examples: Height, length, volume, time.
   • Tests:
     • Ratio Test: Check if one value is twice another.
     • Zero Test: Check if zero means none of the quantity.

Conclusion

• Understanding data types and measurement levels is crucial for appropriate statistical analysis.
• Start by identifying if data meets nominal level, then progress to ordinal, interval, and ratio levels by applying additional criteria.