Q: A pie chart is constructed to represent the educational attainment of U.S. residents in 2021. If 24% of the population has a Bachelor's degree, what is the degree measure of the sector for this category? Use $$ \text{Degrees} = \text{Relative Frequency} \times 360 .$$

$$ 0.24 \times 360 = 86.4 $$ degrees

Q: When organizing continuous quantitative data into classes, which of the following is the correct formula for determining class width?

$$ \text{Class Width} = \frac{\text{Largest Data Value} - \text{Smallest Data Value}}{\text{Number of Classes}} $$

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 with the following frequencies for four categories: A (10), B (20), C (30), D (40), what is the relative frequency for category C? Use the formula $$ 	ext{Relative Frequency} = \frac{	ext{Frequency of the category}}{	ext{Sum of all frequencies}} .$$

Accepted Answer

$$ \frac{30}{100} = 0.3 $$

Question 3

Which of the following statements about bar graphs and histograms is correct?

Accepted Answer

Bar graphs are used for qualitative data and the bars do not touch; histograms are used for quantitative data and the bars touch.

Question 4

A pie chart is constructed to represent the educational attainment of U.S. residents in 2021. If 24% of the population has a Bachelor's degree, what is the degree measure of the sector for this category? Use $$ 	ext{Degrees} = 	ext{Relative Frequency} 	imes 360 .$$

Accepted Answer

$$ 0.24 	imes 360 = 86.4 $$ degrees

Question 5

When organizing continuous quantitative data into classes, which of the following is the correct formula for determining class width?

Accepted Answer

$$ 	ext{Class Width} = \frac{	ext{Largest Data Value} - 	ext{Smallest Data Value}}{	ext{Number of Classes}} $$

Question 6

A histogram of parking fines in New York City shows most fines are between $$200 and 225$$, with frequencies tapering off on both sides. Which shape best describes this distribution?

Accepted Answer

Bell-shaped

Question 7

Which of the following is an advantage of a stem-and-leaf plot over a histogram?

Accepted Answer

A stem-and-leaf plot preserves the original data values.

Question 8

A cumulative frequency distribution for continuous data displays:

Accepted Answer

The total number of observations less than or equal to the upper class limit of a class.

Question 9

Which of the following best describes a time-series plot?

Accepted Answer

A graph with time on the horizontal axis and the variable of interest on the vertical axis, with points connected by line segments.

Question 10

A bar graph is constructed to compare educational attainment in 1990 and 2021. Why is it important to use relative frequencies rather than frequencies for this comparison?

Accepted Answer

Because the total population sizes are different in 1990 and 2021.

Question 11

Which of the following is a common way that graphs can be misleading?

Accepted Answer

By starting the vertical axis at a value other than 0, exaggerating differences.

Question 12

A pictogram is used to compare the popularity of basketball and soccer. If the area of the basketball is four times that of the soccer ball, but basketball is only twice as popular, what is the main issue with this pictogram?

Accepted Answer

The area exaggerates the difference in popularity, misleading the viewer.

Question 13

Which of the following guidelines should be followed to avoid misleading graphics?

Accepted Answer

Avoid three-dimensional charts, as they can distort the data.

Question 14

If a cumulative relative frequency ogive is constructed, what is plotted on the y-axis?

Accepted Answer

The cumulative relative frequency for each class.

Question 15

A frequency polygon is constructed by plotting points at which coordinates?

Accepted Answer

At the class midpoints (x-axis) and the frequencies (y-axis).

Question 16

Which of the following is NOT a recommended practice when constructing a good statistical graphic?

Accepted Answer

Using more than one design in the same graphic to draw attention.

Question 17

A distribution is described as 'skewed right.' Which of the following best describes its appearance?

Accepted Answer

The tail to the right of the peak is longer than the tail to the left.

Question 18

Why should open-ended classes (such as '65 and over') be used with caution in frequency distributions?

Accepted Answer

Because the last class has no upper class limit, making it difficult to interpret the distribution's shape.

Question 19

Which of the following is a correct statement about the use of side-by-side bar graphs?

Accepted Answer

They are useful for comparing relative frequencies between two or more groups.

Organizing and Summarizing Data: Graphical and Tabular Methods in Statistics

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