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

$$\text{Relative Frequency} = \frac{\text{Class Frequency}}{\text{Sample Size}}$$

Q: A frequency distribution has 7 classes, with the lowest class limit 155 and class width 36. What is the upper class limit of the third class?

$$155 + 2 \times 36 - 1 = 226$$

Question 1

Given a data set with a minimum value of 12 and a maximum value of 87, you are asked to construct a frequency distribution with 8 classes. What is the appropriate class width to use?

Accepted Answer

$$\frac{87-12}{8} = 9.375$$, so round up to $$10$$

Question 2

Which of the following best describes the 'frequency' in a frequency distribution table?

Accepted Answer

The number of data entries in each class

Question 3

If a class in a frequency distribution has a lower class limit of 21 and a class width of 5, what is the upper class limit for this class?

Accepted Answer

$$21 + 5 - 1 = 25$$

Question 4

A frequency distribution has the following lower class limits: 10, 20, 30, 40, 50. What is the class width?

Accepted Answer

$$20 - 10 = 10$$

Question 5

Which of the following statements about histograms is TRUE?

Accepted Answer

Consecutive bars must touch to indicate continuous data

Question 6

Given the following class: 40-49, what is the midpoint of this class?

Accepted Answer

$$\frac{40 + 49}{2} = 44.5$$

Question 7

A frequency distribution for commute times (in minutes) has 7 classes, with the lowest value 15 and the highest value 90. What is the class width?

Accepted Answer

$$\frac{90 - 15}{7} = 10.71$$, so round up to $$11$$

Question 8

If a frequency distribution has 6 classes and the range of the data is 30, what is the class width?

Accepted Answer

$$\frac{30}{6} = 5$$

Question 9

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

Accepted Answer

$$	ext{Relative Frequency} = \frac{	ext{Class Frequency}}{	ext{Sample Size}}$$

Question 10

A data set has the following class boundaries: 10.5-20.5, 20.5-30.5, 30.5-40.5. What is the class width?

Accepted Answer

$$20.5 - 10.5 = 10$$

Question 11

In constructing a frequency distribution, why is it important to round up the class width to the next whole number?

Accepted Answer

To ensure all data values are included in the classes

Question 12

If a frequency distribution has the following frequencies: 5, 8, 8, 5, 4, what is the sample size?

Accepted Answer

$$5 + 8 + 8 + 5 + 4 = 30$$

Question 13

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

Accepted Answer

Bars are separated by gaps to show discrete data

Question 14

Given a class with lower class limit 55 and upper class limit 61, what is the class midpoint?

Accepted Answer

$$\frac{55 + 61}{2} = 58$$

Question 15

A frequency distribution has class midpoints of 15, 20, 25, 30, 35. What is the class width?

Accepted Answer

$$20 - 15 = 5$$

Question 16

If the range of a data set is 50 and you want 5 classes, what is the class width?

Accepted Answer

$$\frac{50}{5} = 10$$

Question 17

Which of the following best describes the cumulative frequency for a class?

Accepted Answer

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

Question 18

A frequency distribution has 7 classes, with the lowest class limit 155 and class width 36. What is the upper class limit of the third class?

Accepted Answer

$$155 + 2 	imes 36 - 1 = 226$$

Question 19

If a histogram is constructed for a data set of ages grouped in intervals of 10 years, which of the following is a valid reason for using a histogram instead of a bar chart?

Accepted Answer

A histogram is used for quantitative data with continuous intervals, and bars must touch to show continuity

Frequency Distributions and Histograms in Statistics

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