Q: What is the formula for calculating the percentage for a category in a frequency distribution?

$$\text{Percentage} = \text{Relative frequency} \times 100\%$$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table that shows how data are partitioned among several categories by listing the categories along with the number (frequency) of data values in each of them.

Question 2

Given a data set with a minimum value of 83 and a maximum value of 325, and you want to create 5 classes for a frequency distribution, what is the appropriate class width?

Accepted Answer

$$\frac{325 - 83}{5} = 48.4$$, rounded up to 50

Question 3

What is the formula for calculating the percentage for a category in a frequency distribution?

Accepted Answer

$$	ext{Percentage} = 	ext{Relative frequency} 	imes 100\%$$

Question 4

A sample of 30 people was asked their favorite donut variety. 8 chose glazed, 7 chose filled, 5 chose frosted, 3 chose plain, and 7 chose other. What is the relative frequency of 'frosted'?

Accepted Answer

$$\frac{5}{30} = 0.167$$

Question 5

Which of the following is NOT a feature of a histogram?

Accepted Answer

It is used to display categorical (qualitative) data.

Question 6

What is the difference between a bar graph and a histogram?

Accepted Answer

A bar graph is used for categorical data, while a histogram is used for quantitative data.

Question 7

If a histogram is bell-shaped and symmetric, what type of distribution does the data likely have?

Accepted Answer

Normal distribution

Question 8

A distribution is said to be skewed to the right (positively skewed) if:

Accepted Answer

It has a longer right tail.

Question 9

Which graph is most appropriate for displaying the distribution of a single qualitative variable?

Accepted Answer

Bar graph

Question 10

What is a Pareto chart?

Accepted Answer

A bar graph for categorical data with bars arranged in descending order according to frequencies.

Question 11

Which of the following is a feature of a dotplot?

Accepted Answer

It is usually possible to recreate the original list of data values.

Question 12

In a stem-and-leaf plot, what does the 'stem' represent?

Accepted Answer

The leftmost digit(s) of each data value.

Question 13

Which of the following is true about cumulative frequency distributions?

Accepted Answer

The frequency for each class is the sum of the frequencies for that class and all previous classes.

Question 14

A frequency polygon differs from a histogram in that:

Accepted Answer

It uses line segments connected to points above class midpoints instead of bars.

Question 15

If the sum of the percentages in a relative frequency distribution is 99.8%, what is the most likely explanation?

Accepted Answer

Rounding errors in the calculation of percentages.

Question 16

Which of the following graphs is best for showing the proportion of each category in a whole?

Accepted Answer

Pie chart

Question 17

A city administration wants to know the distribution of vehicles owned by households. If the data are: 0, 1, 2, 3, 4, 5 vehicles, which type of frequency distribution is most appropriate?

Accepted Answer

Single-value class frequency distribution

Question 18

Which of the following is a correct formula for finding the class midpoint?

Accepted Answer

$$	ext{Class midpoint} = \frac{	ext{Lower class limit} + 	ext{Upper class limit}}{2}$$

Question 19

In a histogram, the presence of gaps between bars can indicate:

Accepted Answer

The data may come from two or more different populations.

Question 20

Which of the following is a feature of a stemplot?

Accepted Answer

It retains the original data values and shows the shape of the distribution.

Exploring Data with Tables and Graphs: Frequency Distributions and Graphical Summaries

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