Chapter 2.3

When summarizing graphs of categorical​ data, report the​ _______ and describe the​ _______.

variability

Suppose a group of school age children is​ asked, "Which of these three ice cream flavors do you like the​ most: vanilla,​ chocolate, or​ strawberry?" Describe a bar graph of their responses that would have the least amount of variability. Also describe a bar graph that would have the most variability. Describe a bar graph of their responses that would have the least amount of variability. Choose the correct answer below.

A bar graph with the least variability would be one in which the children favored one particular​ flavor, for example chocolate.

Which of the following is not true regarding bar charts and​ histograms?

A bar chart is used for numerical variables while a histogram is used for categorical variables.

Suppose a group of school age children is​ asked, "Which of these three ice cream flavors do you like the​ most: vanilla,​ chocolate, or​ strawberry?" Describe a bar graph of their responses that would have the least amount of variability. Also describe a bar graph that would have the most variability.Describe a bar graph that would have the most variability. Choose the correct answer below

A bar graph with the most variability would be one in which the same

What are Pareto​ charts?

Bar charts that are sorted from most frequent to least frequent

What are two commonly used graphs to display the distribution of a sample of categorical​ data?

Bar graph and pie chart

One of the authors wanted to determine the effect of changing answers on​multiple-choice tests. She studied the tests given by another​ professor, who had told his students before their exams that if they had doubts about an answer they had​ written, they would be better off not changing their initial answer. The author went through the exams to look for​ erasures, which indicate that the first choice was changed. In these​ tests, there is only one correct answer for each question. Use the bar chart to answer the question below.

No

The accompanying table gives the percent of market controlled by the most popular Internet browsers in one year. Sketch an appropriate graph of the​distribution, and comment on its important features

Pie chart and Pareto chart Browser 1 controls the highest market share.

A categorical variable is only called bimodal under what​ circumstances?

Two categories are nearly tied for most frequent outcomes.

Because the human eye has a difficult time judging how much area is taken up by the​ wedge-shaped slice of a pie​ chart, which of the following is true of pie​ charts?

Pie charts are not commonly used by statisticians or in scientific settings.

Data on obesity rates for adults in a certain region are displayed in the bar plot for three age groups. Complete parts​ (a) and​ (b) below

a) The age group that has the highest rate of obesity is 40-59because it has the tallest bars. b)The obesity rates for women are slightly higher in the 20-39 and 60+age groups. The obesity rate for men is higher in the 40-59 age group.

A survey asked gun owners what percentage of the time they had a loaded gun easily within reach when at home. The results for male gun owners are displayed in a bar chart and a pie chart. Complete parts​ (a) and​ (b) below.

a) The difference is approximately 10. b)It is easier to use a bar chart because you can compare values using the heights of the​ bars, whereas it can be hard to determine which of two slices in a pie chart is larger when they are close in size and not adjacent to each other

Data on the percentage of adults living in a certain area who meet the federal aerobic fitness​ (AF) and muscle strengthening​ (MS) standards are displayed in the bar plot. Complete parts​ (a) and​ (b) below

a)Fitness rates are slightly higher in Region 2 than in the other three regions. b) In each​ region, aerobic fitness rates were higher than​muscle-strengthening rates.

According to an​organization, there are five leading causes of preventable death in a region. They are shown in the graph to the​ right, where HBP is High Blood​Pressure, TU is Tobacco​Use, HBG is High Blood​Glucose, PA is Physical​Activity, and OO and Overweight and Obesity. Use the graph to complete parts​ (a) through​ (e).

a. Estimate how many preventable deaths result from high blood pressure. Approximately 88 million preventable deaths in one year result from high blood pressure. ​(Round to one decimal place as​ needed.) b. Estimate how many preventable deaths result from tobacco use. Approximately 44 million preventable deaths in one year result from tobacco use. ​(Round to one decimal place as​ needed.) c. Does this graph support the theory that the greatest rate of preventable death comes from overweight and​ obesity, as some people have​ claimed? No, the graph does not support the theory that the greatest rate of preventable death comes from overweight and​ obesity, because overweight and obesity do not cause the greatest number of preventable deaths. d. This is a bar chart with a special name because of the decreasing order of the bars. What is that​ name? Pareto chart

When thinking about the variability of a categorical​ distribution, it is sometimes useful to think of the word​ _______.

diversity

When describing the distribution of a categorical​ variable, the category that appears most often is called the​ _____.

mode