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

$$ \text{Relative Frequency} = \frac{\text{Frequency of Category}}{\text{Total Frequency}} $$

Question 1

Which of the following best describes the main difference between a bar chart and a histogram?

Accepted Answer

A bar chart displays frequencies for categorical variables, while a histogram displays frequencies for numerical variables.

Question 2

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

Accepted Answer

Categorical data where the sum of all categories represents a whole.

Question 3

In a bar chart, what does the height of each bar represent?

Accepted Answer

The frequency or relative frequency of the category.

Question 4

Given a survey where 7 students are 'Unknown', 3 are 'Sophomore', 4 are 'Junior', 5 are 'Senior', and 1 is 'Graduate', what is the relative frequency of 'Senior'?

Accepted Answer

$$ \frac{5}{20} = 0.25 $$

Question 5

Which of the following is a key feature of a Pareto chart?

Accepted Answer

Bars are arranged from tallest to shortest.

Question 6

A bar chart for internet usage among teens shows two categories ('Almost Constantly' and 'Several Times a Day') each at about 45%, and two other categories much lower. What is the mode of this distribution?

Accepted Answer

Both 'Almost Constantly' and 'Several Times a Day'

Question 7

Which of the following best describes 'variability' in a categorical distribution?

Accepted Answer

How spread out the frequencies are among the categories.

Question 8

If a pie chart shows one category taking up nearly the entire circle, what can you conclude about the variability of the distribution?

Accepted Answer

The variability is low because most data falls into one category.

Question 9

A bar chart for School A shows several ethnic groups with significant percentages, while School B's chart shows nearly 100% Hispanic. Which school has higher variability in ethnic composition?

Accepted Answer

School A

Question 10

Which of the following is NOT a correct statement about bar charts?

Accepted Answer

Bars in a bar chart must touch each other.

Question 11

A survey asks people to identify their economic class. The bar chart shows 1% 'Don't Know', 30% 'Lower', 45% 'Middle', and 15% 'Upper'. What is the mode?

Accepted Answer

'Middle'

Question 12

Which graphical display would be most appropriate to show the distribution of favorite ice cream flavors among 100 students?

Accepted Answer

Bar chart

Question 13

If a bar chart shows three candy choices with nearly equal bar heights, what does this indicate about the variability?

Accepted Answer

High variability

Question 14

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

Accepted Answer

$$ 	ext{Relative Frequency} = \frac{	ext{Frequency of Category}}{	ext{Total Frequency}} $$

Question 15

Which of the following is NOT a characteristic of a categorical variable?

Accepted Answer

It can take on any value within a range.

Question 16

A bar chart shows the following frequencies for favorite colors: Red (10), Blue (15), Green (5), Yellow (20). What is the relative frequency of Blue?

Accepted Answer

$$ \frac{15}{50} = 0.3 $$

Question 17

Which of the following best describes the 'mode' in a categorical distribution?

Accepted Answer

The category with the highest frequency.

Question 18

Why is it inappropriate to use a histogram for categorical data?

Accepted Answer

Because histograms are designed for numerical data with intervals.

Question 19

A pie chart shows five categories. If one slice is much larger than the others, what does this suggest about the distribution?

Accepted Answer

One category is much more common than the others.

Question 20

Which of the following is a valid reason for using relative frequency instead of frequency in a bar chart?

Accepted Answer

To compare distributions with different total sample sizes.

Visualizing and Describing Categorical Data in Introductory Statistics

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