Q: When constructing a frequency distribution for numerical data, which of the following is the correct formula for determining the class interval (width)?

$\text{Class Interval} = \dfrac{\text{Range}}{\text{Number of Classes}}$

Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that cross-tabulates the responses of two or more categorical variables to study patterns between them.

Question 2

A manufacturer records the daily high temperature for 20 days: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 58. If the range is calculated as $	ext{Range} = 	ext{Highest value} - 	ext{Lowest value}$, what is the range of this data set?

Accepted Answer

$	ext{Range} = 58 - 12 = 46$

Question 3

When constructing a frequency distribution for numerical data, which of the following is the correct formula for determining the class interval (width)?

Accepted Answer

$	ext{Class Interval} = \dfrac{	ext{Range}}{	ext{Number of Classes}}$

Question 4

A summary table is most appropriate for which type of data?

Accepted Answer

Categorical data with a single variable

Question 5

Which graphical display is best suited for visualizing the relationship between two numerical variables?

Accepted Answer

Scatter plot

Question 6

A bar chart is used to visualize which of the following?

Accepted Answer

The frequencies or percentages of categories in a categorical variable

Question 7

Which of the following statements about histograms is TRUE?

Accepted Answer

Histograms are used for numerical data and have no gaps between adjacent bars.

Question 8

A Pareto chart is most useful for which of the following purposes?

Accepted Answer

Comparing the frequencies of categories in descending order to identify the 'vital few' causes

Question 9

If you want to compare the distribution of invoice errors across different invoice sizes using a graphical display, which chart would be most appropriate?

Accepted Answer

Side by side bar chart

Question 10

Which of the following is a best practice when constructing visualizations?

Accepted Answer

Begin the scale for a vertical axis at zero and use a constant scale.

Question 11

A frequency polygon is most useful for:

Accepted Answer

Comparing the distribution of a numerical variable across two or more groups

Question 12

Which of the following is NOT a reason to use a frequency distribution?

Accepted Answer

It is the only way to display categorical data.

Question 13

When comparing two groups with different sample sizes, which type of distribution should you use?

Accepted Answer

Relative frequency or percentage distribution

Question 14

A stem-and-leaf display is particularly useful for:

Accepted Answer

Visualizing the distribution and concentration of numerical data

Question 15

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

Accepted Answer

$	ext{Relative Frequency} = \dfrac{	ext{Frequency of the class}}{	ext{Total number of observations}}$

Question 16

A time series plot is best used for which of the following scenarios?

Accepted Answer

Studying patterns in the values of a numerical variable over time

Question 17

If you are given a data set with 100 values, what is a reasonable number of classes to use in a frequency distribution?

Accepted Answer

Between 5 and 15

Question 18

Which of the following is a potential pitfall when choosing class boundaries for a frequency distribution, especially with small data sets?

Accepted Answer

Different class boundaries may provide different pictures of the same data.

Question 19

In a contingency table, the percentage of a cell based on the total number of observations is called:

Accepted Answer

Overall percentage

Question 20

Which chart type is most appropriate for visualizing the proportion of each category in a single categorical variable?

Accepted Answer

Pie chart

Organizing and Visualizing Variables in Business Statistics

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