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

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

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

$$ \text{Relative frequency} = \frac{\text{Frequency of class}}{\text{Sample size}} $$

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 entries in each class.

Question 2

Given a data set with a minimum value of 120, a maximum value of 340, and you want to create 8 classes, what is the appropriate class width? (Round up to the next convenient number.)

Accepted Answer

$$ \frac{340 - 120}{8} = 27.5 $$, so the class width should be 28.

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 class limits: 100-119, 120-139, 140-159. What is the class width?

Accepted Answer

$$ 120 - 100 = 20 $$

Question 5

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

Accepted Answer

$$ 	ext{Relative frequency} = \frac{	ext{Frequency of class}}{	ext{Sample size}} $$

Question 6

In constructing a frequency histogram, what does the vertical axis represent?

Accepted Answer

The frequencies of the classes.

Question 7

Suppose you have the following frequencies for five classes: 3, 7, 12, 8, 5. What is the cumulative frequency for the fourth class?

Accepted Answer

$$ 3 + 7 + 12 + 8 = 30 $$

Question 8

Which of the following statements about class boundaries is correct?

Accepted Answer

Class boundaries are the values that separate classes without forming gaps between them.

Question 9

A cumulative frequency graph (ogive) is most useful for which of the following purposes?

Accepted Answer

Determining the number of data values below a particular value.

Question 10

You are given a frequency distribution with class limits 50-59, 60-69, 70-79, and frequencies 4, 7, 9. What is the relative frequency of the second class?

Accepted Answer

$$ \frac{7}{4+7+9} = \frac{7}{20} = 0.35 $$

Question 11

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

Accepted Answer

Calculate the mean and standard deviation of the data.

Question 12

A frequency polygon differs from a histogram in that:

Accepted Answer

It uses line segments to connect class midpoints at the class frequencies.

Question 13

If the lower class limit of the first class is 150 and the class width is 25, what is the lower class limit of the fourth class?

Accepted Answer

$$ 150 + 3 	imes 25 = 225 $$

Question 14

Which of the following best describes a relative frequency histogram?

Accepted Answer

A histogram where the vertical axis measures the relative frequencies of the classes.

Question 15

A researcher collects data on the number of hours students study per week and wants to display the percentage of students in each interval. Which graph should she use?

Accepted Answer

Relative frequency histogram

Question 16

If a class has a lower class limit of 200 and an upper class limit of 249, what is the midpoint of the class?

Accepted Answer

$$ \frac{200 + 249}{2} = 224.5 $$

Question 17

Which of the following is a correct statement about cumulative frequency?

Accepted Answer

The cumulative frequency of the last class is equal to the sample size.

Question 18

A frequency distribution for exam scores is constructed with class limits 60-69, 70-79, 80-89, 90-99. If the frequency for 80-89 is 12 and the total sample size is 40, what is the relative frequency for this class?

Accepted Answer

$$ \frac{12}{40} = 0.3 $$

Question 19

When constructing an ogive, what value is plotted on the horizontal axis for each class?

Accepted Answer

The upper class boundary

Descriptive Statistics: Frequency Distributions and Their Graphs

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