Q: Given a data set with a minimum value of 120, a maximum value of 370, and a requirement for 10 classes, what is the appropriate class width? (Round up to the next whole number.) $$\text{Class width} = \frac{\text{Maximum value} - \text{Minimum value}}{\text{Number of classes}}$$

$$\text{Class width} = \frac{370 - 120}{10} = 26$$

Q: What is the midpoint of the class interval 191–226?

$$\text{Midpoint} = \frac{191 + 226}{2} = 208.5$$

Question 1

Which of the following best describes a frequency distribution table?

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 370, and a requirement for 10 classes, what is the appropriate class width? (Round up to the next whole number.)

$$	ext{Class width} = \frac{	ext{Maximum value} - 	ext{Minimum value}}{	ext{Number of classes}}$$

Accepted Answer

$$	ext{Class width} = \frac{370 - 120}{10} = 26$$

Question 3

What is the midpoint of the class interval 191–226?

Accepted Answer

$$	ext{Midpoint} = \frac{191 + 226}{2} = 208.5$$

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?

$$	ext{Relative frequency} = \frac{	ext{Class frequency}}{	ext{Total frequency}}$$

Accepted Answer

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

Question 5

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

Accepted Answer

The bars are separated by gaps to show different classes.

Question 6

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

Accepted Answer

Showing the cumulative total of frequencies up to each class boundary.

Question 7

Given the following class limits: 263–298, what are the class boundaries?

Accepted Answer

$$262.5$$ and $$298.5$$

Question 8

Which type of graph would be most appropriate to display the cumulative number of defective products produced each day in a factory?

Accepted Answer

Ogive

Question 9

If the cumulative frequency for the third class is 15 and the frequency for the fourth class is 7, what is the cumulative frequency for the fourth class?

Accepted Answer

$$15 + 7 = 22$$

Question 10

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

Accepted Answer

Class midpoints versus class frequencies, connected by straight lines.

Question 11

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

Accepted Answer

To ensure that all data values are included in the classes.

Question 12

Which of the following best describes the difference between a frequency histogram and a relative frequency histogram?

Accepted Answer

A frequency histogram displays frequencies, while a relative frequency histogram displays proportions or percentages.

Question 13

A data set of 50 exam scores is grouped into 5 classes. If the lowest score is 40 and the highest is 90, what is the minimum class width required?

$$	ext{Class width} = \frac{	ext{Maximum value} - 	ext{Minimum value}}{	ext{Number of classes}}$$

Accepted Answer

$$\frac{90 - 40}{5} = 11$$

Question 14

Which of the following is a valid reason for using an ogive in environmental science?

Accepted Answer

To study the cumulative distribution of rainfall over a period.

Question 15

If a frequency distribution has classes 10–19, 20–29, 30–39, what is the class width?

Accepted Answer

$$20 - 10 + 1 = 10$$

Question 16

Which of the following graphs is best for displaying the distribution of a small set of quantitative data, such as the number of pets owned by 15 students?

Accepted Answer

Dot plot

Question 17

In a frequency distribution, what is the cumulative frequency of the last class always equal to?

Accepted Answer

The total number of data entries (sample size)

Question 18

A business wants to evaluate whether it has met its quarterly sales targets. Which graph would best help visualize the cumulative progress toward the target?

Accepted Answer

Ogive

Question 19

Which of the following is a correct step in constructing a frequency polygon?

Accepted Answer

Plot the class midpoints against the class frequencies and connect the points with straight lines.

Question 20

Why is it important to choose an appropriate number of classes (between 5 and 20) when constructing a frequency distribution?

Accepted Answer

Too few classes may obscure patterns, while too many classes may make patterns difficult to detect.

Descriptive Statistics: Frequency Distributions and Graphs

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