Q: When organizing continuous quantitative data into classes, what is the formula for class width?

$$\text{Class width} = \frac{\text{Largest data value} - \text{Smallest data value}}{\text{Number of classes}}$$

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 the following frequency table for M&M colors, what is the relative frequency of yellow M&Ms?

Brown: 12, Yellow: 10, Red: 9, Orange: 6, Blue: 3, Green: 5

Accepted Answer

$$\frac{10}{45} \approx 0.2222$$

Question 3

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

Accepted Answer

Bar graphs are used for qualitative data, while histograms are used for quantitative data.

Question 4

A Pareto chart is a special type of bar graph. What makes it unique?

Accepted Answer

Bars are drawn in decreasing order of frequency or relative frequency.

Question 5

Why should relative frequencies be used instead of frequencies when comparing two data sets of different sizes in a side-by-side bar graph?

Accepted Answer

Relative frequencies account for different sample sizes, making comparisons fair.

Question 6

Which of the following best describes a pie chart?

Accepted Answer

A circle divided into sectors, with each sector proportional to the frequency of a category.

Question 7

When organizing continuous quantitative data into classes, what is the formula for class width?

Accepted Answer

$$	ext{Class width} = \frac{	ext{Largest data value} - 	ext{Smallest data value}}{	ext{Number of classes}}$$

Question 8

Which of the following is an advantage of a stem-and-leaf plot over a histogram?

Accepted Answer

A stem-and-leaf plot preserves the original data values.

Question 9

A dot plot is most useful for which type of data?

Accepted Answer

Small sets of discrete quantitative data.

Question 10

Which of the following histograms represents a distribution that is skewed right?

Accepted Answer

A histogram where the tail to the right of the peak is longer than the tail to the left.

Question 11

Suppose you are constructing a time-series plot of the closing prices of a stock over several years. What should be on the horizontal axis?

Accepted Answer

Time (e.g., years)

Question 12

Which of the following is a common way that a graph can be misleading?

Accepted Answer

Truncating the vertical axis to exaggerate differences.

Question 13

A student creates a pie chart where one sector is much larger than it should be, exaggerating the proportion of students who study 6-10 hours per week. What is this an example of?

Accepted Answer

A misleading graph.

Question 14

Which of the following guidelines should be followed to avoid misleading graphics?

Accepted Answer

Avoid using three-dimensional effects that can distort the data.

Question 15

A frequency table for the number of cars per household is given as follows: 0 cars: 4, 1 car: 13, 2 cars: 22, 3 cars: 7, 4 cars: 3, 5 cars: 1. What is the relative frequency for households with 3 cars?

Accepted Answer

$$\frac{7}{50} = 0.14$$

Question 16

Which of the following best describes a bell-shaped distribution?

Accepted Answer

The highest frequency occurs in the middle and frequencies tail off to the left and right.

Question 17

If you want to compare the educational attainment of the U.S. population in 1990 and 2013, which type of graph would be most appropriate?

Accepted Answer

A side-by-side bar graph using relative frequencies.

Question 18

Which of the following is NOT a guideline for constructing good graphics?

Accepted Answer

Use more than one design in the same graphic to draw attention.

Question 19

A histogram is constructed for the time between eruptions at Old Faithful. The smallest value is 672 seconds and the largest is 738 seconds. If you want 7 classes, what is the class width?

Accepted Answer

$$\frac{738 - 672}{7} = 9.43$$, round up to 10

Question 20

Which of the following statements about stem-and-leaf plots is TRUE?

Accepted Answer

They allow you to reconstruct the original data set.

Summarizing Data in Tables and Graphs: Introductory Statistics Study Notes

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