Q: Which of the following is the correct formula for calculating the class boundaries between two adjacent classes?

$$ \text{Class Boundaries (CB)} = \frac{\text{Upper Class Limit of Previous Class} + \text{Lower Class Limit of Next Class}}{2} $$

Question 1

A frequency table for commute times in a city shows the following bins: 0-14, 15-29, 30-44, 45-59, 60-74, 75-89, 90-104. If 3 commuters fall into the 15-29 minute bin out of a total of 20 commuters, what is the relative frequency for this bin?

Accepted Answer

$$ \frac{3}{20} = 0.15 $$

Question 2

Given the class interval 20-29, what is the class midpoint?

Accepted Answer

$$ \frac{20 + 29}{2} = 24.5 $$

Question 3

A frequency table for commute times in Boston shows the following frequencies: 3 (15-24 min), 3 (25-34 min), 3 (35-44 min), 3 (45-54 min), 2 (55-64 min), 2 (65-74 min), 2 (75-84 min), 2 (85-94 min). What is the cumulative frequency after the 45-54 minute bin?

Accepted Answer

$$ 3 + 3 + 3 + 3 = 12 $$

Question 4

Which of the following best describes a histogram?

Accepted Answer

A graph that displays the shape of the distribution of quantitative data using bars whose heights correspond to frequency counts in bins.

Question 5

If a histogram of exam scores is bell-shaped and symmetric, what can you infer about the distribution of the scores?

Accepted Answer

The distribution is approximately normal.

Question 6

A dataset of arm circumferences is plotted as a histogram. The histogram is skewed to the right. What does this indicate about the data?

Accepted Answer

There are more values clustered at the lower end, with a longer tail to the right.

Question 7

Which of the following is the correct formula for calculating the class boundaries between two adjacent classes?

Accepted Answer

$$ 	ext{Class Boundaries (CB)} = \frac{	ext{Upper Class Limit of Previous Class} + 	ext{Lower Class Limit of Next Class}}{2} $$

Question 8

A pie chart is most appropriate for which type of data?

Accepted Answer

Categorical data where the size of each slice is proportional to the frequency count for the category.

Question 9

In a frequency distribution, what is the lower class limit?

Accepted Answer

The smallest value that can belong to a class interval.

Question 10

A time-series graph is used to:

Accepted Answer

Reveal information about trends over time.

Question 11

If a frequency table for commute times in New York and Boise shows that 75.8% of Boise commuters have commute times in the lowest two classes, while only 28.9% of New York commuters do, what can you infer?

Accepted Answer

Boise has a much higher proportion of short commute times compared to New York.

Question 12

Which of the following is NOT a feature of a histogram?

Accepted Answer

It shows the relationship between two categorical variables.

Question 13

A stemplot (stem-and-leaf plot) is particularly useful because:

Accepted Answer

It retains the original data values and shows the shape of the distribution.

Question 14

Which of the following best describes a bar graph?

Accepted Answer

A graph of bars of equal width to show frequencies of categories of categorical data.

Question 15

If a dataset's histogram is skewed to the left, what does this indicate?

Accepted Answer

The data have a longer tail on the left side.

Question 16

Which of the following is the correct formula for calculating the relative frequency for a class?

Accepted Answer

$$ 	ext{Relative Frequency} = \frac{	ext{Frequency for a class}}{	ext{Sum of all frequencies}} $$

Question 17

A dotplot is most useful for which of the following purposes?

Accepted Answer

Displaying the shape of the distribution of data and allowing recreation of the original list of data values.

Question 18

Which of the following is a potential pitfall when interpreting graphs?

Accepted Answer

Graphs can be constructed to mislead by distorting the scale or omitting context.

Question 19

In constructing a frequency table, why must bins have the same width and not overlap?

Accepted Answer

To ensure that each data point is counted only once and the distribution is accurately represented.

Question 20

A relative frequency histogram differs from a regular histogram in that:

Accepted Answer

The vertical axis is marked with relative frequencies instead of actual frequencies.

Exploring Data with Tables and Graphs: Frequency Distributions, Histograms, and Data Visualization

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