One Quantitative Variable: Introduction
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).
The overall pattern of the distribution of a quantitative variable is described by its shape, center, 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
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.