Statistics Chapter 2

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

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

mode(s); variability

A distribution of a variable in which most of the values are relatively small but that also has a few very large values is called​ ________.

right-skewed

If a sample of people were asked how many hours of TV they watched in a typical​ week, what shape would the data distribution be expected to​ have?

right-skewed

Which of the following is not a difference between bar charts and​ histograms?

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

What are Pareto​ charts?

Bar charts that are sorted from most frequent to least frequent

What is the most common trick to mislead readers of bar​ graphs?

Change the scale of the vertical axis so that it does not start at 0.

Which of the following is not a way in which the Internet is influencing statistical​ graphics?

Decreasing the use of misleading graphics

When examining the shape of a distribution of numerical​ data, which of the following is not one of the three basic characteristics of a​ distribution's shape?

How many numbers are in the data set.

All methods used for visualizing distributions are based on which of the​ following?

Make a mark that indicates how many times each value occurred in the data set.

What is the first step in almost every investigation of​ data?

Make an appropriate graph.

According to the ancient Roman architect​ Vitruvius, a​ person's armspan​ (the distance from fingertip to fingertip with the arms stretched​ wide) is approximately equal to his or her height. For​ example, people 5 feet tall tend to have an armspan of 5 feet.​ Explain, then, why the distribution of armspans for a class containing roughly equal numbers of men and women might be bimodal.

Men and women tend to have different heights and therefore different armspans.

Values so large or so small that they do not fit into the pattern of the distribution are called​ what?

Outliers

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.

​"Relative frequency" is the same as which of the​ following?

Proportion

What​ two-step process is used to examine​ distributions?

See the data and summarize it

The distribution of​ in-state annual tuition for all colleges and universities in the United States is bimodal. What is one possible reason for this​ bimodality?

The distribution might be bimodal because private colleges and public colleges tend to differ in amount of tuition.

Predict the shape of the distribution of the numbers of times a group of 500 people eat breakfast in one week.

The distribution will be​ left-skewed. Most people will report eating breakfast every​ day, with a few reporting various values less than 7.

A teacher asks 90 students who drive how many speeding tickets they received in the last year. Predict the shape of the distribution and explain.

The distribution will be​ right-skewed. Most people will have no​ tickets, but there will be a few people with​ 1, 2,​ 3, or more tickets.

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

Two categories are nearly tied for most frequent outcomes.

The existence of multiple mounds in a distribution is sometimes a sign of which of the​ following?

Two very different groups have been combined into a single collection

A stemplot is often useful in which of the following​ cases?

When technology is not available and the data set is not large

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

bar graph and pie chart

In a​ histogram, observations are grouped into intervals called​ ____.

bins

Changing the width of bins in a histogram​ _______.

changes the shape of the histogram.

The​ _____ organizes data by recording all the values observed in a sample as well as how many times each value was observed.

distribution of a sample

When examining a distribution of numerical​ data, which of the following is not a feature that needs to be​ considered?

each individual value