Q: A frequency distribution has the following intervals: 40–59, 60–75, 76–82, 83–94, 95–99. What is the formula to calculate the class midpoint for any interval?

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

Q: If the ages of patients in a study range from 27 to 62 and you want 8 classes, what is the formula for determining the class width?

$$\frac{\text{Max value} - \text{Min value}}{\text{Number of classes}}$$

Question 1

Given the following frequency distribution for math test scores, what are the class boundaries for the interval 40–59?

Scores | Number of students
40–59 | 2
60–75 | 4
76–82 | 6
83–94 | 15
95–99 | 5

Accepted Answer

$$40.5, 59.5$$

Question 2

For the same frequency distribution, what is the class midpoint for the interval 40–59?

Accepted Answer

$$49.5$$

Question 3

What are the class boundaries for the interval 95–99 in the given frequency distribution?

Accepted Answer

$$95.5, 100.5$$

Question 4

A medical research team studied the ages of 34 patients who had strokes caused by stress. If you are to construct a frequency distribution with 8 classes beginning with a lower class limit of 25, what is the class width you should use?

Accepted Answer

$$rac{62 - 25}{7} = 5.2857$$

Question 5

In a survey, 20 people were asked how many magazines they had purchased during the previous year. If you construct a histogram with 4 classes, a class width of 10, and a lower class limit of -0.5, what is the center value of the third class?

Accepted Answer

$$24.5$$

Question 6

When constructing a frequency distribution, why is it important to use equal class widths?

Accepted Answer

It ensures that each class represents an equal range of data, making comparisons between classes meaningful.

Question 7

Given the following class interval: 60–75, what is the class midpoint?

Accepted Answer

$$67.5$$

Question 8

If a histogram is constructed with 5 classes, a lower class limit of 19.5, and a class width of 10, what is the upper class boundary of the third class?

Accepted Answer

$$48.5$$

Question 9

A frequency distribution has the following intervals: 40–59, 60–75, 76–82, 83–94, 95–99. What is the formula to calculate the class midpoint for any interval?

Accepted Answer

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

Question 10

Why might a researcher choose to use class boundaries instead of class limits when constructing a histogram?

Accepted Answer

Class boundaries prevent gaps between bars in the histogram, accurately representing continuous data.

Question 11

If the ages of patients in a study range from 27 to 62 and you want 8 classes, what is the formula for determining the class width?

Accepted Answer

$$\frac{	ext{Max value} - 	ext{Min value}}{	ext{Number of classes}}$$

Question 12

A histogram is constructed for magazine purchases with classes: -0.5–9.5, 9.5–19.5, 19.5–29.5, 29.5–39.5. What is the midpoint of the second class?

Accepted Answer

$$14.5$$

Question 13

If a class interval is 83–94, what are the class boundaries?

Accepted Answer

$$82.5, 94.5$$

Question 14

Which of the following best describes a frequency distribution?

Accepted Answer

A summary table that shows how data are distributed across different intervals or classes.

Question 15

In constructing a histogram, what is the effect of choosing too few classes?

Accepted Answer

The data may be oversimplified, hiding important patterns or variations.

Question 16

If the class width is 10 and the lower class limit of the first class is -0.5, what is the lower class limit of the fourth class?

Accepted Answer

$$29.5$$

Question 17

A frequency distribution is constructed for ages with 8 classes, starting at 25 and ending at 62. What is the upper class limit of the last class?

Accepted Answer

$$62$$

Question 18

Which of the following is NOT a reason to use a frequency distribution when analyzing data?

Accepted Answer

To display individual data points for each observation.

Question 19

If a class interval is 76–82, what is the class width?

Accepted Answer

$$7$$

Question 20

When constructing a histogram for ages with 5 classes, a lower class limit of 19.5, and a class width of 10, what is the midpoint of the fifth class?

Accepted Answer

$$59.5$$

Exploring Data with Tables and Graphs: Practice Problems and Concepts

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