Question

The U.S. Department of Education reported that $14 \%$ of adults were classified as being below a basic literacy level, $29 \%$ were classified as being at a basic literacy level, $44 \%$ were classified as being at an intermediate literacy level, and $13 \%$ were classified as being at a proficient level ( 2003 National Assessment of \mathrm{\{} A d u l t ~ L i t e r a c y ) . ~ a. Is the variable literacy level categorical or numerical? b. Construct a bar chart to display the given data on literacy level. c. Would it be appropriate to display the given information using a dotplot? Explain why or why not.

Name: Problem 33, Chapter 1: Introduction to Statistics and Data Analysis
Uploaded: 2023-09-01T22:47:20-08:00
Channel: Donna Densmore

   The U.S. Department of Education reported that $14 \%$ of adults were classified as being below a basic literacy level, $29 \%$ were classified as being at a basic literacy level, $44 \%$ were classified as being at an intermediate literacy level, and $13 \%$ were classified as being at a proficient level ( 2003 National Assessment of \mathrm{\{} A d u l t ~ L i t e r a c y ) . ~
a. Is the variable literacy level categorical or numerical?
b. Construct a bar chart to display the given data on literacy level.
c. Would it be appropriate to display the given information using a dotplot? Explain why or why not.

Introduction to Statistics and Data Analysis

Roxy Peck, Chris… 5th Edition

Chapter 1, Problem 33

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Solved by Expert Donna Densmore

09/01/2023

Step 1

The variable literacy level is categorical because it represents different categories or groups (below basic, basic, intermediate, and proficient) rather than numerical values. b. To construct a bar chart, we will represent each category on the x-axis and the Show more…

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The U.S. Department of Education reported that $14 \%$ of adults were classified as being below a basic literacy level, $29 \%$ were classified as being at a basic literacy level, $44 \%$ were classified as being at an intermediate literacy level, and $13 \%$ were classified as being at a proficient level ( 2003 National Assessment of \mathrm{\{} A d u l t ~ L i t e r a c y ) . ~ a. Is the variable literacy level categorical or numerical? b. Construct a bar chart to display the given data on literacy level. c. Would it be appropriate to display the given information using a dotplot? Explain why or why not.

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Key Concepts

Categorical vs. Numerical Variables

This concept distinguishes between types of data. Categorical data consist of distinct groups or categories, such as literacy levels, while numerical data are quantifiable and ordered. Recognizing the nature of the variable helps in selecting an appropriate method for analysis and visualization.

Bar Chart

A bar chart is a graphical representation used to display and compare the frequency or proportion of different categories. Each category is represented by a bar whose height is proportional to its value, making it a suitable choice for visualizing data like literacy levels that are divided into groups.

Dotplot

A dotplot is a type of chart typically used for showing the distribution of numerical data or small datasets. Although it can be adapted for categorical data, it is less ideal for representing categorical variables since it may not clearly convey differences among discrete groups compared to a bar chart.

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