Q: Given a dataset with a minimum value of 5 and a maximum value of 90, and you want to create 7 classes for a frequency distribution, what is the appropriate class width? Use the formula $$\text{Class width} = \frac{\text{maximum value} - \text{minimum value}}{\text{number of classes}}$$ and round up to a convenient number.

$$\text{Class width} = \frac{90 - 5}{7} = 12.14$$, rounded up to 15

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

$$\text{Relative frequency} = \frac{\text{class frequency}}{\text{total number of observations}}$$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table that lists all possible values of a variable and the number of times each value occurs.

Question 2

Given a dataset with a minimum value of 5 and a maximum value of 90, and you want to create 7 classes for a frequency distribution, what is the appropriate class width? Use the formula $$	ext{Class width} = \frac{	ext{maximum value} - 	ext{minimum value}}{	ext{number of classes}}$$ and round up to a convenient number.

Accepted Answer

$$	ext{Class width} = \frac{90 - 5}{7} = 12.14$$, rounded up to 15

Question 3

What is the main advantage of using a relative frequency distribution instead of a simple frequency distribution?

Accepted Answer

It allows for easier comparison between datasets of different sizes.

Question 4

A cumulative frequency distribution for commute times shows that 24 people have commute times less than 30 minutes. If the total sample size is 50, what is the cumulative relative frequency for this class?

Accepted Answer

$$\frac{24}{50} = 0.48$$

Question 5

Which of the following is NOT a benefit of using a histogram to display data?

Accepted Answer

It shows the exact value of every data point.

Question 6

A histogram of commute times is shown to be skewed to the right. Which of the following best describes this distribution?

Accepted Answer

The distribution has a longer tail on the right side.

Question 7

If a frequency distribution has a gap (one or more classes with zero frequency), what might this indicate about the data?

Accepted Answer

The data may come from two or more different populations.

Question 8

Given the following class limits: 0-14, 15-29, 30-44, what is the class midpoint for the class 15-29?

Accepted Answer

$$\frac{15 + 29}{2} = 22$$

Question 9

Which of the following best describes a normal distribution as seen in a histogram?

Accepted Answer

The frequencies start low, increase to a maximum, and then decrease, forming a symmetric bell shape.

Question 10

A relative frequency histogram is different from a regular histogram in that:

Accepted Answer

The vertical axis shows proportions or percentages instead of counts.

Question 11

Suppose you are constructing a frequency distribution and your calculated class width is 12.1. According to best practices, what should you do?

Accepted Answer

Round up to a convenient number, such as 15.

Question 12

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

Accepted Answer

$$	ext{Relative frequency} = \frac{	ext{class frequency}}{	ext{total number of observations}}$$

Question 13

A normal quantile plot is used to assess normality. Which of the following patterns would indicate that the data are NOT normally distributed?

Accepted Answer

The points do not lie reasonably close to a straight line.

Question 14

If a histogram shows two distinct clusters of data with a gap in between, what is the most likely explanation?

Accepted Answer

The data may come from two different populations.

Question 15

Which of the following is NOT a step in constructing a frequency distribution?

Accepted Answer

Calculate the mean and median of the data.

Question 16

A dataset of arm circumferences is displayed in a histogram that is symmetric and bell-shaped. What can you infer about the distribution?

Accepted Answer

The data are approximately normally distributed.

Question 17

If a histogram of commute times has a long tail to the left, how would you describe the skewness?

Accepted Answer

The distribution is skewed to the left (negatively skewed).

Question 18

Which of the following is a reason why class boundaries are used in frequency distributions?

Accepted Answer

To avoid gaps between classes for continuous data.

Question 19

A cumulative frequency table for 'minutes to get ready' shows a cumulative frequency of 21 for the 10-14 minute class. What does this mean?

Accepted Answer

21 people take 14 minutes or less to get ready.

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

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