Statistics begins with knowing what kind of data you have, because the data type determines what questions you can answer and what tools you should use. Categorical data describe groups or labels, such as favorite color, blood type, or class rank. Quantitative data describe amounts or counts, such as height, number of siblings, or reaction time.
Classifying data correctly helps you choose the right graph, summary, and interpretation.
Key Facts
- Categorical data describe qualities, labels, or groups, not measurable amounts.
- Quantitative data describe numerical values that can be counted or measured.
- Nominal data have categories with no natural order, such as eye color or car brand.
- Ordinal data have ordered categories, such as small, medium, large or survey ratings from 1 to 5.
- Discrete quantitative data take countable values, such as number of pets, while continuous quantitative data can take any value in an interval, such as mass or time.
- Mean = sum of values / number of values, and it is appropriate for many quantitative data sets but not for nominal categories.
Vocabulary
- Categorical data
- Data that place observations into groups or labels instead of measuring numerical amounts.
- Quantitative data
- Data that give numerical measurements or counts that can be used in arithmetic.
- Nominal data
- Categorical data with groups that do not have a natural order.
- Ordinal data
- Categorical data with groups that have a meaningful order but not necessarily equal spacing.
- Continuous data
- Quantitative data that can take any value within a range, often measured with decimals.
Common Mistakes to Avoid
- Treating category codes as real numbers is wrong because numbers like 1 = red and 2 = blue are labels, so their average has no meaningful interpretation.
- Using a mean for nominal data is wrong because unordered categories cannot be added or divided in a meaningful way.
- Calling every number quantitative is wrong because some numbers, such as jersey numbers or ZIP codes, identify categories rather than measure amounts.
- Using a bar graph and histogram interchangeably is wrong because bar graphs compare categories, while histograms show the distribution of quantitative values across intervals.
Practice Questions
- 1 A survey records the favorite science subject of 40 students: physics 12, biology 10, chemistry 9, astronomy 6, and geology 3. What type of data is this, and what percentage chose physics?
- 2 A data set gives the number of books read last month by 8 students: 0, 1, 2, 2, 3, 4, 4, 8. Is the data discrete or continuous, and what is the mean number of books read?
- 3 A hospital records patient pain levels as none, mild, moderate, or severe. Classify the data type and explain which graph and summary would be more appropriate than calculating a mean.