Q: Suppose you are constructing a frequency distribution for continuous data with a minimum value of 65 and a maximum value of 322.61. If you want 11 classes, what is the formula for the class width, and what is the recommended next step?

$$ \text{Class Width} = \frac{\text{Maximum Value} - \text{Minimum Value}}{\text{Number of Classes}} $$; round up to a convenient number.

Q: A frequency polygon is constructed by plotting points at the class midpoints. What is the formula for the class midpoint?

$$ \text{Class Midpoint} = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2} $$

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

$$ \frac{30}{100} = 0.30 $$

Question 3

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

Accepted Answer

In a bar graph, the bars do not touch; in a histogram, the bars touch.

Question 4

A physical therapist collects data on the body part requiring rehabilitation for 30 patients. She organizes the data into a table showing the number of patients for each body part. What type of table has she created?

Accepted Answer

A frequency distribution

Question 5

When constructing a pie chart, how do you determine the degree measure of a sector for a category with relative frequency $$ r $$? Use the formula $$ 	ext{Degrees} = r 	imes 360 .$$

Accepted Answer

$$ r 	imes 360 $$

Question 6

A histogram is constructed for the number of customers arriving at a restaurant in 15-minute intervals. The data are discrete and range from 1 to 11. What is the main reason for using a histogram instead of a bar graph in this context?

Accepted Answer

A histogram is appropriate for quantitative data and shows the distribution of frequencies across intervals.

Question 7

Which of the following best describes a distribution that is 'skewed right'?

Accepted Answer

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

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 is a potential problem with using a three-dimensional pie chart to display data?

Accepted Answer

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

Question 10

Suppose you are constructing a frequency distribution for continuous data with a minimum value of 65 and a maximum value of 322.61. If you want 11 classes, what is the formula for the class width, and what is the recommended next step?

Accepted Answer

$$ 	ext{Class Width} = \frac{	ext{Maximum Value} - 	ext{Minimum Value}}{	ext{Number of Classes}} $$; round up to a convenient number.

Question 11

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

Accepted Answer

Data measured at different points in time.

Question 12

Which of the following is a guideline for constructing good graphics?

Accepted Answer

Avoid three-dimensional charts as they can distract and mislead the reader.

Question 13

A frequency polygon is constructed by plotting points at the class midpoints. What is the formula for the class midpoint?

Accepted Answer

$$ 	ext{Class Midpoint} = \frac{	ext{Lower Class Limit} + 	ext{Upper Class Limit}}{2} $$

Question 14

Which of the following is a reason why a bar graph with a vertical axis that does not start at zero can be misleading?

Accepted Answer

It exaggerates the differences between categories.

Question 15

A stem-and-leaf plot is constructed for a data set. 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 16

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

Accepted Answer

Using three-dimensional effects to make the graph more attractive.

Question 17

If a bar graph is used to compare educational attainment in 1990 and 2021, why should relative frequencies be used instead of frequencies?

Accepted Answer

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

Question 18

Which of the following best describes an ogive?

Accepted Answer

A graph that represents the cumulative frequency or cumulative relative frequency for the class.

Question 19

A misleading pictogram shows a basketball with an area four times larger than a soccer ball, even though basketball participation is only about twice that of soccer. What is the main issue with this graphic?

Accepted Answer

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

Organizing and Summarizing Data: Tables and Graphs in Introductory Statistics

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