Q: If the range of a data set is $$10$$ and you want to create $$k = 5$$ classes, what is the formula for the class width?

$$\text{width} = \frac{10}{5}$$

Question 1

Which of the following is the most appropriate graphical representation for visualizing the distribution of a categorical variable such as political party preference?

Accepted Answer

Pie chart

Question 2

A bar graph is used to display the results of a survey on students' favorite sports teams. What type of variable is being visualized?

Accepted Answer

Categorical variable

Question 3

Given a data set of survival times (in days) for lung cancer patients, which of the following would be the best way to visualize the distribution of this numerical variable?

Accepted Answer

Dotplot

Question 4

A histogram is constructed for the salaries of NHL players. The first class interval is $$0.5 \u003c 2.0$$ million with a relative frequency of $$0.6000. If $$the width of this class is $$1.5$$, what is the density for this class?

Accepted Answer

$$0.4000$$

Question 5

Why is a density histogram preferred over a relative frequency histogram when class intervals are not of equal width?

Accepted Answer

Because it allows the total area under the histogram to equal 1, making comparisons between classes fair regardless of width

Question 6

Suppose you have a data set with a minimum value of $$0.5$$ and a maximum value of $$12.5. If $$you want to create $$k = 5$$ classes, what is the class width?

Accepted Answer

$$2.4$$

Question 7

In a pie chart showing the breakdown of gas prices, the 'Taxes' segment is 32%. What does this mean in the context of the data?

Accepted Answer

32% of the gas price is due to taxes

Question 8

A histogram of NHL salaries is right-skewed. What does this indicate about the distribution of salaries?

Accepted Answer

Most players have low to moderate salaries, with a few having very high salaries

Question 9

If you randomly select an NHL player from the 2016-2017 season, what is the probability that their salary is less than $$3$$ million, given that the area under the density histogram for this range is $$0.67$$?

Accepted Answer

$$0.67$$

Question 10

You are given a data set of the average number of views per post (in millions) for TikTok influencers. If the class interval $$1 \u003c 2$$ has a relative frequency of $$0.20$$ and a width of $$1$$, what is the density for this class?

Accepted Answer

$$0.20$$

Question 11

Which of the following is NOT a guideline for constructing a frequency distribution?

Accepted Answer

Assign each data point to multiple classes

Question 12

A student creates a 3D pie chart to display the distribution of a single categorical variable. What is a potential issue with this approach?

Accepted Answer

It is difficult to interpret the proportions accurately in more than two dimensions

Question 13

If a histogram is constructed with class intervals of unequal width, which of the following statements is true?

Accepted Answer

The height of each bar should represent the density, calculated as $$\frac{	ext{relative frequency}}{	ext{class width}}$$

Question 14

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

Accepted Answer

Comparing the distribution of a numerical variable across two small samples

Question 15

If you combine the upper two classes $$9 \u003c 10$$ and $$10 \u003c 16 in a $$histogram of TikTok influencer views, what must you do to calculate the density of the new combined class?

Accepted Answer

Add the frequencies and divide by the new class width

Question 16

Which of the following best describes a left-skewed distribution?

Accepted Answer

The tail on the left side of the distribution is longer than the right

Question 17

A bar graph is constructed to show the number of students in each political party category, broken down by gender. What type of data visualization is this?

Accepted Answer

A grouped bar graph

Question 18

If the range of a data set is $$10$$ and you want to create $$k = 5$$ classes, what is the formula for the class width?

Accepted Answer

$$	ext{width} = \frac{10}{5}$$

Question 19

In a sample of 150 TikTok influencers, the class $$4 \u003c 6$$ million views contains 30 influencers. What is the proportion of influencers in this class?

Accepted Answer

$$0.20$$

Question 20

Which of the following is a key difference between a frequency histogram and a density histogram?

Accepted Answer

A frequency histogram uses counts, while a density histogram uses densities so that the total area is 1

Visual Representations of Data in Statistics: Categorical and Numerical Variables

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