Question

Find the class boundaries, midpoints, and widths for each class. a. 32-38 b. 86-104 c. 895–905 d. 12.3-13.5 e. 3.18-4.96

Answer 1

Class boundaries are the numbers used to separate classesThe class midpoint is equal to the average of the upper class limit and the lower class limit.Class width is the spacing among groups in a frequency distribution table.The class boundaries, midpoints, and widths for each class are provided.

Step-by-step explanation:

The class boundaries, midpoints, and widths for each class are as follows:

a. Class boundaries: 31.5-38.5; Midpoint: 34.5; Width: 7

b. Class boundaries: 85.5-104.5; Midpoint: 95; Width: 19

c. Class boundaries: 894.5-905.5; Midpoint: 900; Width: 11

d. Class boundaries: 12.15-13.85; Midpoint: 13.0; Width: 1.7

e. Class boundaries: 3.085-4.085; Midpoint: 3.585; Width: 1.0

Answer 2

Class boundaries, midpoints, and widths are calculated for each of the given classes. Boundaries are set to minimize gaps, midpoints represent the center of the classes, and widths illustrate the range of each class. Examples are provided for every listed class interval.

Step-by-step explanation:

The concepts of class boundaries, midpoints, and class widths are essential in organizing data into a frequency distribution, which is often used to create histograms. To find these elements for the given classes, use the following methods:

• The class boundaries are the values that separate classes without leaving gaps between them. For continuous data, each upper class boundary is the same as the next lower class boundary.
• The midpoint of a class (also called the class mark) is the average of the lower and upper class limits. It can be graphed on the x-axis and is calculated by adding the upper and lower limits and dividing by two.
• The class width is the difference between the upper and lower boundaries of a class.

For the given classes:

1. 32-38: The class boundaries are 31.5 and 38.5, midpoint is 35, and width is 7.
2. 86-104: The class boundaries are 85.5 and 104.5, midpoint is 95, and width is 18.
3. 895–905: The class boundaries are 894.5 and 905.5, midpoint is 900, and width is 10.
4. 12.3-13.5: The class boundaries are 12.25 and 13.55, midpoint is 12.9, and width is 1.2.
5. 3.18-4.96: The class boundaries are 3.175 and 4.965, midpoint is 4.07, and width is 1.785.