Univariate Data
Univariate data is a data set that records values for just one variable. For example, measuring the heights of every student in a class gives you univariate data — there's only one quantity being tracked.
Univariate data consists of observations on a single variable across a set of individuals or cases. Analysis of univariate data focuses on describing the distribution of that variable through its shape, center, spread, and any unusual features such as outliers or gaps. Common numerical summaries include the mean, median, standard deviation, and five-number summary, while common graphical displays include histograms, dotplots, boxplots, and stemplots.
Worked Example
Problem: A teacher records the test scores of 10 students: 72, 85, 90, 68, 95, 88, 76, 82, 91, 78. Describe the center and spread of this univariate data set.
Step 1: Confirm this is univariate data. There is only one variable being measured — test score — so this qualifies as univariate.
Step 2: Arrange the values in order to help identify the center and spread.
Step 3: Find the mean by adding all values and dividing by the number of observations.
Step 4: Find the median. With 10 values, the median is the average of the 5th and 6th values in order.
Step 5: Describe the spread using the range.
Answer: The center of the data is approximately 82.5 (mean) or 83.5 (median), and the scores span a range of 27 points, from 68 to 95.
Visualization
Why It Matters
Univariate data analysis is the foundation of statistics. Before you can explore relationships between two or more variables, you need to understand how to describe a single variable's distribution. In AP Statistics, nearly every inference procedure — confidence intervals, significance tests — begins with understanding the behavior of one variable at a time.
Common Mistakes
Mistake: Confusing univariate data with bivariate data when two measurements are collected.
Correction: If you record both height and weight for each person, that is bivariate data (two variables). Univariate data involves only one variable, such as just the heights.
Mistake: Thinking that a single number counts as univariate data.
Correction: Univariate refers to one variable, not one observation. You still need multiple observations of that single variable to have a data set worth analyzing.