One Quantitative Variable: Introduction

CO-4: Distinguish among different measurement scales, choose the appropriate descriptive and inferential statistical methods based on these distinctions, and interpret the results.

Distribution of One Quantitative Variable

LO 4.4: Using appropriate graphical displays and/or numerical measures, describe the distribution of a quantitative variable in context: a) describe the overall pattern, b) describe striking deviations from the pattern

In the previous section, we explored the distribution of a categorical variable using graphs (pie chart, bar chart) supplemented by numerical measures (percent of observations in each category).

In this section, we will explore the data collected from a quantitative variable, and learn how to describe and summarize the important features of its distribution.

We will learn how to display the distribution using graphs and discuss a variety of numerical measures.

An introduction to each of these topics follows.


To display data from one quantitative variable graphically, we can use either a histogram or boxplot.

We will also present several “by-hand” displays such as the stemplot and dotplot (although we will not rely on these in this course).

Numerical Measures

The overall pattern of the distribution of a quantitative variable is described by its shapecenter, and spread.

By inspecting the histogram or boxplot, we can describe the shape of the distribution, but we can only get a rough estimate for the center and spread.

A description of the distribution of a quantitative variable must include, in addition to the graphical display, a more precise numerical description of the center and spread of the distribution.

In this section we will learn:

  • how to display the distribution of one quantitative variable using various graphs;
  • how to quantify the center and spread of the distribution of one quantitative variable with various numerical measures;
  • some of the properties of those numerical measures;
  • how to choose the appropriate numerical measures of center and spread to supplement the graph(s); and
  • how to identify potential outliers in the distribution of one quantitative variable
  • We will also discuss a few measures of position (also called measures of location). These measures
    • allow us to quantify where a particular value is relative to the distribution of all values
    • do provide information about the distribution itself
    • also use the information about the distribution to learn more about an INDIVIDUAL
We will present the material in a logical sequence which builds in difficulty, intermingling discussion of visual displays and numerical measures as we proceed.

Before reading further, try this interactive applet which will give you a preview of some of the topics we will be learning about in this section on exploratory data analysis for one quantitative variable.