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

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

Question 1

Which of the following best describes a frequency distribution?

Accepted Answer

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

Question 2

Given a data set with a minimum value of 12 and a maximum value of 92, and you want to create 8 classes, what is the class width you should use?

Accepted Answer

$$\frac{92-12}{8} = 10 ($$Round up to 11)

Question 3

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

Accepted Answer

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

Question 4

A frequency distribution has the following classes: 10-19, 20-29, 30-39. What is the lower class boundary of the first class?

Accepted Answer

$$9.5$$

Question 5

If a class in a frequency distribution has a frequency of 7 and the sample size is 35, what is the relative frequency of that class?

Accepted Answer

$$\frac{7}{35} = 0.2$$

Question 6

Which graph is best used to display the cumulative frequency of each class?

Accepted Answer

Ogive

Question 7

Why must consecutive bars in a frequency histogram touch each other?

Accepted Answer

To emphasize the continuity of the data values.

Question 8

A data set has a minimum value of 45 and a maximum value of 125. You want to create 5 classes. What is the range and what class width should you use?

Accepted Answer

Range: $$125 - 45 = 80$$, Class width: $$\frac{80}{5} = 16 ($$Round up to 16)

Question 9

In constructing a frequency polygon, what values are plotted on the horizontal axis?

Accepted Answer

Class midpoints

Question 10

A cumulative frequency graph (ogive) for cell phone screen times shows a steep increase between 262.5 and 334.5 minutes. What does this indicate about the data?

Accepted Answer

A large number of data values fall within the 262.5 to 334.5 minute interval.

Question 11

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

Accepted Answer

Calculate the mean and standard deviation.

Question 12

If the lower class limit of the first class is 50 and the class width is 12, what is the lower class limit of the third class?

Accepted Answer

$$50 + 2 	imes 12 = 74$$

Question 13

Which of the following statements about class boundaries is correct?

Accepted Answer

Class boundaries are used to separate classes without forming gaps between them.

Question 14

A frequency histogram is constructed for a data set. What does the height of each bar represent?

Accepted Answer

The frequency of the class.

Question 15

Which graph would you use to quickly compare the proportion of data in each class?

Accepted Answer

Relative frequency histogram

Question 16

If you are using technology (such as a TI-84 Plus calculator) to construct a histogram, which list should contain the class midpoints?

Accepted Answer

L1

Question 17

A frequency distribution for exam scores has the following classes: 60-69, 70-79, 80-89, 90-99. If 15 students scored between 80 and 89, and the total number of students is 60, what is the relative frequency for the 80-89 class?

Accepted Answer

$$\frac{15}{60} = 0.25$$

Question 18

Which of the following best describes the purpose of using a frequency polygon?

Accepted Answer

To emphasize the continuous change in frequencies across classes.

Question 19

In a real-world scenario, a hospital records the number of minutes patients spend in the waiting room. If the most common range is 20-30 minutes, what does this indicate about the frequency distribution?

Accepted Answer

The class 20-30 minutes has the highest frequency.

Descriptive Statistics: Frequency Distributions and Their Graphs

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