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 and a maximum value of 340, and you want to create 8 classes, what is the appropriate class width?

Accepted Answer

$$\frac{340 - 120}{8} = 27.5$$, so round up to 28

Question 3

What is the formula for the midpoint of a class with a lower class limit $$L$$ and an upper class limit $$U$$?

Accepted Answer

$$\frac{L + U}{2}$$

Question 4

If a class in a frequency distribution has a frequency of 8 and the total number of data entries is 40, what is the relative frequency of that class?

Accepted Answer

$$\frac{8}{40} = 0.2$$

Question 5

Which of the following statements about histograms is TRUE?

Accepted Answer

The bars in a histogram must touch because the data is continuous.

Question 6

What is the cumulative frequency for the third class if the frequencies for the first three classes are 5, 7, and 9?

Accepted Answer

$$5 + 7 + 9 = 21$$

Question 7

Which graph is most appropriate for displaying the cumulative frequency of a data set?

Accepted Answer

Ogive

Question 8

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

Accepted Answer

Class midpoints

Question 9

If the range of a data set is 90 and you want 6 classes, what is the class width?

Accepted Answer

$$\frac{90}{6} = 15$$, so round up to 15

Question 10

Which of the following best describes a relative frequency histogram?

Accepted Answer

A histogram where the vertical axis shows the proportion or percentage of data in each class.

Question 11

Why are class boundaries used when constructing a histogram?

Accepted Answer

To ensure that consecutive bars touch and there are no gaps between classes.

Question 12

A data set of exam scores has the following class limits: 50-59, 60-69, 70-79, 80-89. What is the lower class boundary for the first class?

Accepted Answer

$$49.5$$

Question 13

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

Accepted Answer

Calculate the mean and median of the data set.

Question 14

If the cumulative frequency for the fourth class is 25 and the cumulative frequency for the third class is 18, what is the frequency of the fourth class?

Accepted Answer

$$25 - 18 = 7$$

Question 15

A researcher wants to display the distribution of daily water usage (in liters) for 100 households. Which graphical display is most appropriate?

Accepted Answer

Frequency histogram

Question 16

Which of the following is a correct interpretation of a steep segment in an ogive?

Accepted Answer

There is a large increase in cumulative frequency over that class interval.

Question 17

If a frequency distribution has class limits 100-119, 120-139, 140-159, what is the class width?

Accepted Answer

$$120 - 100 = 20$$

Question 18

Which of the following is a reason to round up the class width when constructing a frequency distribution?

Accepted Answer

To ensure all data values are included and classes do not overlap.

Question 19

A frequency distribution for the number of hours spent studying per week is constructed with 5 classes. The frequencies are 2, 5, 8, 10, and 5. What is the cumulative frequency for the fourth class?

Accepted Answer

$$2 + 5 + 8 + 10 = 25$$

Descriptive Statistics: Frequency Distributions and Graphical Displays

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