Univariate data

Univariate data records one variable per observational unit, so what you hold is a single column of values and what you can describe is a single distribution. That fixes the available questions: shape, center, spread and unusual values. Nothing else is on the table, because there is no second measurement on the same individuals to set each value against.

Nine patients wait 4, 6, 7, 7, 9, 11, 12, 15 and 34 minutes. The total is 105, so $\bar{x} = 105/9 = 11.67$ minutes, and the median is the fifth value in order, 9 minutes. The gap between those two centers, and the 34 sitting clear of everything else, is the kind of thing a univariate description reports. What it cannot report is why that patient waited 34 minutes, since no other variable was recorded.

The wrong sentence is "our survey collected age, income and city, so nothing about it is univariate." Univariate describes the question, not the file. Almost every real data table has many columns, and you work through them one at a time: the distribution of age is univariate, and so is the distribution of income. The moment you ask whether income changes with age you have left univariate analysis, and no new data were collected at that point.

That second question is bivariate data, where a scatterplot or a two-way table replaces the dotplot and direction, form and strength become askable. Comparing one quantitative variable across groups sits in between: side-by-side boxplots of wait time at three clinics still describe one variable's distribution within each group, which the course treats as comparing distributions, topic 1.9.

Dotplots, histograms, stemplots and boxplots are univariate displays, topics 1.5 and 1.8, and describing what one of them shows is topic 1.6. The single variable can be categorical instead, in which case the display is a bar graph and the summary is counts and proportions rather than center and spread.