In Exercises 5–8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B.
8.

Verified step by step guidance

1. Step 1: Identify the class width. The class width is calculated by subtracting the lower boundary of one class from the lower boundary of the next class. For example, subtract 100 from 200 to get the class width: 200 - 100 = 100.
2. Step 2: Calculate the class midpoints. The midpoint of each class is found by averaging the lower and upper boundaries of the class. For example, for the first class (100–199), the midpoint is (100 + 199) / 2 = 149.5. Repeat this for all classes.
3. Step 3: Determine the class boundaries. The boundaries are calculated by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class. For example, for the first class (100–199), the boundaries are 99.5 and 199.5. Repeat this for all classes.
4. Step 4: Sum the frequencies to find the total number of individuals included in the summary. Add all the frequencies together: 25 + 92 + 28 + 0 + 2.
5. Step 5: Verify the calculations and ensure all values (class width, midpoints, boundaries, and total frequency) are consistent with the given data.

Key Concepts

Class Width

Class width refers to the range of values that each class interval covers in a frequency distribution. It is calculated by subtracting the lower boundary of a class from its upper boundary. For example, in the class interval 100-199, the class width is 199 - 100 = 99. Understanding class width is essential for accurately interpreting the distribution of data.

Class Midpoint

The class midpoint is the value that lies in the middle of a class interval and is calculated by averaging the upper and lower boundaries of the class. For instance, for the class interval 100-199, the midpoint is (100 + 199) / 2 = 149.5. Class midpoints are useful for summarizing data and performing further statistical analysis.

Class Boundaries

Class boundaries are the values that separate one class interval from another in a frequency distribution. They are typically calculated by taking the average of the upper limit of one class and the lower limit of the next class. For example, the boundary between the classes 100-199 and 200-299 would be 199.5. Class boundaries help in accurately grouping data and avoiding overlaps between classes.