# 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.

**Video:**One Quantitative Variable (4:16)

**Related SAS Tutorials**

- 5A – (3:01) Numeric Measures using PROC MEANS
- 5B – (4:05) Creating Histograms and Boxplots using SGPLOT
- 5C – (5:41) Creating QQ-Plots and other plots using UNIVARIATE

**Related SPSS Tutorials**

- 5A – (8:00) Numeric Measures using EXPLORE
- 5B – (2:29) Creating Histograms and Boxplots
- 5C – (2:31) Creating QQ-Plots and PP-Plots

## 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.

## Graphs

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 **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**

- allow us to quantify where a particular value is relative to the

**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.

**Interactive Applet:**Analyze One Quantitative Variable with this One-Variable Statistical Calculator