Q: Given a data set of 50 parking fines ranging from $$65 to 322.61$$, you decide to create classes starting at $$50 with a class width of 25. $$What is the formula for determining the class width, and why might you round up the result?

Class width = $$\frac{\text{Largest data value} - \text{Smallest data value}}{\text{Number of classes}}$$; rounding up ensures all data are included and classes are easy to interpret.

Q: A pie chart is constructed to display the educational attainment of U.S. adults in 2021. If 9% of adults are not high school graduates, what is the degree measure of the sector representing this category?

$$0.09 \times 360 = 32.4$$ degrees

Question 1

Which of the following best describes a frequency distribution for qualitative data?

Accepted Answer

A table that lists each category of data and the number of occurrences for each category.

Question 2

Given a data set of 50 parking fines ranging from $$65 to 322.61$$, you decide to create classes starting at $$50 with a class width of 25. $$What is the formula for determining the class width, and why might you round up the result?

Accepted Answer

Class width = $$\frac{	ext{Largest data value} - 	ext{Smallest data value}}{	ext{Number of classes}}$$; rounding up ensures all data are included and classes are easy to interpret.

Question 3

A bar graph is constructed to compare the educational attainment of U.S. adults in 1990 and 2021. Why should relative frequencies be used instead of frequencies when comparing these two years?

Accepted Answer

Because the total population sizes are different, making frequencies misleading for comparison.

Question 4

Which of the following is a key difference between a histogram and a bar graph?

Accepted Answer

In a histogram, the rectangles touch each other; in a bar graph, the rectangles do not touch.

Question 5

A pie chart is constructed to display the educational attainment of U.S. adults in 2021. If 9% of adults are not high school graduates, what is the degree measure of the sector representing this category?

Accepted Answer

$$0.09 	imes 360 = 32.4$$ degrees

Question 6

Which of the following best describes a cumulative frequency distribution?

Accepted Answer

A table that displays the total number of observations less than or equal to each category or class.

Question 7

A stem-and-leaf plot is constructed for the percentage of persons living in poverty by state. What is one advantage of a stem-and-leaf plot over a histogram?

Accepted Answer

The raw data can be retrieved from the stem-and-leaf plot.

Question 8

Which of the following is NOT a guideline for constructing good graphics?

Accepted Answer

Use three-dimensional charts to make the data more visually appealing.

Question 9

A time-series plot is most appropriate for which type of data?

Accepted Answer

Data measured at different points in time.

Question 10

A misleading graph uses a vertical axis that does not start at zero, exaggerating the difference between two values. What is the best way to correct this issue?

Accepted Answer

Start the vertical axis at zero or clearly indicate truncation with a symbol.

Question 11

Which of the following best describes a Pareto chart?

Accepted Answer

A bar graph where the bars are drawn in decreasing order of frequency or relative frequency.

Question 12

Suppose you are constructing a frequency polygon. What is the x-coordinate for each point you plot?

Accepted Answer

The class midpoint, calculated as $$\frac{	ext{Lower class limit} + 	ext{Next lower class limit}}{2}.$$

Question 13

Which of the following is a potential problem with using three-dimensional pie charts?

Accepted Answer

They can distort the perceived size of categories, making some appear larger than they are.

Question 14

A dot plot is constructed for the number of customers arriving at a restaurant in 40 intervals. What does each dot above a value represent?

Accepted Answer

One observation of that value.

Question 15

Which of the following is NOT a valid description of the shape of a distribution for quantitative data?

Accepted Answer

Skewed upward

Question 16

Why is it misleading to use area (such as the size of a basketball vs. a soccer ball) to represent frequency in a pictogram?

Accepted Answer

Because the area increases with the square of the radius, exaggerating differences between categories.

Question 17

Which of the following is true about open-ended classes in a frequency distribution?

Accepted Answer

The first class has no lower class limit or the last class has no upper class limit.

Question 18

A cumulative relative frequency distribution shows that 54% of fines were under $200. What does this mean?

Accepted Answer

54% of all observations are less than or equal to $200.

Question 19

Which of the following is a reason to avoid using multiple designs in the same graphic?

Accepted Answer

It can distract the reader and force attention to a specific part of the graph.

Organizing and Summarizing Data: Graphical and Tabular Methods in Statistics

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