Q: What is the formula for calculating the relative frequency for a class in a frequency distribution?

$$\text{Relative frequency} = \frac{\text{class frequency}}{\text{sum of all frequencies}}$$

Question 1

Which of the following best describes the purpose of constructing a frequency distribution for a large data set?

Accepted Answer

To organize and summarize data by showing how data values are distributed among categories or classes.

Question 2

Given a data set with a minimum value of 12 and a maximum value of 38, and you want to create 7 classes, what is the appropriate class width?

Accepted Answer

$$\frac{38-12}{7} = 3.71$$, so round up to 4

Question 3

What is the formula for calculating the relative frequency for a class in a frequency distribution?

Accepted Answer

$$	ext{Relative frequency} = \frac{	ext{class frequency}}{	ext{sum of all frequencies}}$$

Question 4

A histogram is constructed for the IQ scores of a group of students. The frequencies start low, increase to a maximum, and then decrease, with the left and right sides roughly mirroring each other. What is the shape of this distribution?

Accepted Answer

Bell-shaped (normal distribution)

Question 5

Which of the following is a characteristic of a right-skewed (positively skewed) distribution?

Accepted Answer

The right tail is longer than the left tail.

Question 6

If a frequency distribution has class limits of 10–19, 20–29, 30–39, what are the class boundaries for the first class?

Accepted Answer

$$9.5$$ and $$19.5$$

Question 7

A student constructs a histogram for a data set and notices that the vertical axis starts at 50 instead of 0. What is a potential problem with this graph?

Accepted Answer

It may exaggerate differences between frequencies and be misleading.

Question 8

Which type of graph is most appropriate for displaying the relationship between two quantitative variables, such as height and weight?

Accepted Answer

Scatterplot

Question 9

A frequency polygon differs from a histogram in that:

Accepted Answer

It uses line segments connected to points above class midpoints.

Question 10

Which of the following best describes a stemplot (stem-and-leaf plot)?

Accepted Answer

It separates each value into a stem and a leaf to display quantitative data.

Question 11

A time-series graph is most useful for:

Accepted Answer

Displaying how a variable changes over time.

Question 12

Which of the following is a key step in constructing a frequency distribution table?

Accepted Answer

Determine the number of classes and calculate the class width.

Question 13

If a histogram shows two distinct peaks, the distribution is best described as:

Accepted Answer

Bimodal

Question 14

A pie chart is most appropriate for displaying:

Accepted Answer

The proportion of each category in a qualitative data set.

Question 15

Which of the following is a potential issue with using three-dimensional bars or boxes in a graph to represent one-dimensional data?

Accepted Answer

It can exaggerate differences and mislead the viewer.

Question 16

Given the following class limits: 20–29, 30–39, 40–49, what is the class midpoint for the second class?

Accepted Answer

$$\frac{30 + 39}{2} = 34.5$$

Question 17

A relative frequency histogram differs from a regular histogram in that:

Accepted Answer

The vertical axis shows relative frequencies instead of actual frequencies.

Question 18

Which of the following best describes a uniform distribution?

Accepted Answer

All classes have approximately the same frequency.

Question 19

If a scatterplot shows points falling in a descending straight line from left to right, what type of relationship does this indicate?

Accepted Answer

Negative linear relationship

Question 20

Which of the following is NOT a characteristic used to describe the distribution of a data set?

Accepted Answer

Color

Frequency Distributions and Graphs in Introductory Statistics

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