Q: In constructing a frequency distribution, what is the formula for the class midpoint?

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

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

A table showing the frequency of data values within chosen groups or classes.

Question 2

Given the following class limits for a frequency distribution: 20–29, 30–39, 40–49, what is the class width?

Accepted Answer

$$30 - 20 = 10$$

Question 3

If a frequency distribution has the following frequencies: 2, 3, 5, 4, what is the relative frequency of the class with frequency 5?

Accepted Answer

$$\frac{5}{14}$$

Question 4

A dataset has a minimum value of 8 and a maximum value of 71. If you want to create 7 classes, what is the class width?

Accepted Answer

$$\frac{71 - 8}{6}$$

Question 5

In constructing a frequency distribution, what is the formula for the class midpoint?

Accepted Answer

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

Question 6

A call center records the number of customers served per hour for 14 hours: 15, 24, 20, 27, 31, 28, 33, 36, 30, 29, 32, 34, 35, 38. If the base class limit is 15 and the class width is 5, what is the lower class limit of the third class?

Accepted Answer

Question 7

Which of the following is NOT a step in constructing a frequency distribution?

Accepted Answer

Find the mean of the dataset.

Question 8

If a frequency distribution table shows the following relative frequencies: 0.10, 0.20, 0.30, 0.40, what is the total number of measurements?

Accepted Answer

The sum of the frequencies for all classes

Question 9

Given the following frequency distribution for travel time to work (in minutes):

15–25: 156
26–35: 243
36–45: 112
46–55: 72
56–65: 40

What is the class midpoint for the class 36–45?

Accepted Answer

$$\frac{36 + 45}{2} = 40.5$$

Question 10

A sales dataset has values: 819, 899, 900, 973, 975, 1023, 1025, 1087, 1100, 1144, 1223. If you want to create 5 classes, what is the class width?

Accepted Answer

$$\frac{1223 - 819}{4}$$

Question 11

Why is it important to round up the class width when constructing a frequency distribution?

Accepted Answer

To ensure all data values are included within the classes.

Question 12

If you have a dataset with 12 overtime hours worked: 3, 2, 14, 12, 11, 8, 13, 9, 10, 7, 6, 4, and you want to use a lower class limit of 3 and a class width of 2, what is the upper class limit of the third class?

Accepted Answer

7

Question 13

Which of the following best describes a relative frequency distribution?

Accepted Answer

A table showing the percentage of data values in each class.

Question 14

If a class has a lower class limit of 20 and an upper class limit of 29, what is the class midpoint?

Accepted Answer

$$\frac{20 + 29}{2} = 24.5$$

Question 15

A frequency distribution has 5 classes and the lowest data value is 15. If the class width is 7, what is the lower class limit of the fourth class?

Accepted Answer

36

Question 16

When constructing a frequency distribution, what is the first step?

Accepted Answer

Determine the number of classes.

Question 17

If the sum of all frequencies in a frequency distribution is 50, and the frequency for a class is 10, what is the relative frequency for that class?

Accepted Answer

$$\frac{10}{50} = 0.2$$

Question 18

A frequency distribution has classes 10–19, 20–29, 30–39, 40–49. If a data value is 29, which class does it belong to?

Accepted Answer

20–29

Question 19

If you have a dataset with values ranging from 15 to 38 and you want to create 5 classes, what is the class width?

Accepted Answer

$$\frac{38 - 15}{4}$$

Frequency Distributions in Statistics: Concepts, Construction, and Applications

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