$$ \text{Midpoint} = \frac{\text{Lower class limit} + \text{Upper class limit}}{2} $$

$$ \text{Relative frequency} = \frac{\text{Class frequency}}{\text{Sample size}} $$

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table that shows classes or intervals of data with a count of the number of data entries in each class.

Question 2

Given a dataset with a maximum value of 400 and a minimum value of 155, and you want to create 7 classes, what is the class width?

Accepted Answer

$$ \frac{400 - 155}{7} = 35.00 $$, but you must round up to the next whole number, so the class width is $$36$$

Question 3

How do you determine the lower class limits when constructing a frequency distribution?

Accepted Answer

Start with the minimum data value and add the class width repeatedly for each subsequent class.

Question 4

What is the formula for the midpoint of a class in a frequency distribution?

Accepted Answer

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

Question 5

If a class in a frequency distribution has a lower limit of 191 and a class width of 36, what is the lower limit of the next class?

Accepted Answer

$$ 191 + 36 = 227 $$

Question 6

How is the relative frequency of a class calculated?

Accepted Answer

$$ 	ext{Relative frequency} = \frac{	ext{Class frequency}}{	ext{Sample size}} $$

Question 7

What is the cumulative frequency for a class?

Accepted Answer

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

Question 8

Which graph is best used to show the cumulative frequency of each class at its upper class boundary?

Accepted Answer

Ogive (Cumulative Frequency Graph)

Question 9

A frequency polygon is constructed by plotting which values on the horizontal axis?

Accepted Answer

The midpoints of each class

Question 10

If the sum of the frequencies in a frequency distribution does not equal the sample size, what is the most likely error?

Accepted Answer

A data value was omitted or counted incorrectly in the tally process.

Question 11

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

Accepted Answer

Round up the class width to the next convenient number.

Question 12

Why is it important that class intervals in a frequency distribution do not overlap?

Accepted Answer

To ensure each data value is counted in only one class.

Question 13

Given the following class limits: 155-190, 191-226, 227-262, what is the class width?

Accepted Answer

$$ 191 - 155 = 36 $$

Question 14

Which of the following best describes a relative frequency histogram?

Accepted Answer

A histogram where the vertical axis measures the relative frequencies (percentages or decimals) instead of raw frequencies.

Question 15

If a class has a lower limit of 208.5 and an upper limit of 244.5, what is the midpoint?

Accepted Answer

$$ \frac{208.5 + 244.5}{2} = 226.5 $$

Question 16

Which of the following is NOT a correct step in constructing a cumulative frequency graph (ogive)?

Accepted Answer

Plot the cumulative frequencies at the midpoints of each class.

Question 17

A dataset has the following frequencies for five classes: 3, 7, 8, 6, 6. What is the cumulative frequency for the fourth class?

Accepted Answer

$$ 3 + 7 + 8 + 6 = 24 $$

Question 18

In a real-world scenario, why might a researcher choose to use a relative frequency histogram instead of a frequency histogram?

Accepted Answer

To compare distributions from samples of different sizes using percentages or proportions.

Describing Data with Frequency Distributions and Graphs

Study Guide - Practice Questions