The Language of Variation: Variables

Not all variables are the same

• Before you graph or summarize data, you must know what kind of variable you have.
• The big split: categorical 分类 (labels/groups) vs. quantitative 定量 (numbers you can do arithmetic on).
• The type decides which graphs and which summaries make sense.
• Choosing the wrong tool for the type is a classic mistake — so classify first.

Categorical vs. quantitative

• A categorical variable records a group or label: eye color, favorite sport, yes/no.
• A quantitative variable is a measured number you can average: height, age, test score.
• Quick test: does averaging the values make sense? If yes → quantitative; if no → categorical.
• (Zip codes look numeric but are categorical — you'd never average them.)

Categorical variables sort cases into groups; quantitative variables are numbers you can average

Discrete vs. continuous

• Quantitative variables come in two flavors.
• Discrete 离散 variables take countable, separate values (number of siblings: $0,1,2,\dots$).
• Continuous 连续 variables can take any value in a range (height: $170.3$ cm, $170.34$ cm, …).
• Counting → discrete; measuring → usually continuous.

Type dictates the tools

• Categorical → bar charts, pie charts, frequency tables, proportions.
• Quantitative → histograms, dotplots, boxplots, mean, standard deviation.
• Using a quantitative tool (like a mean) on a categorical variable is meaningless.
• So always classify the variable before picking a graph or summary.

Write from a quantitative count

• A survey records eye colour and the number of pets.
• Eye colour is a label. The pet count is a number.