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.
7.

Verified step by step guidance

1. Step 1: Identify the class width. The class width is calculated as the difference between the lower boundary of one class and the lower boundary of the next class. For example, the lower boundary of the first class is 0, and the lower boundary of the second class is 100. Therefore, the class width is 100.
2. Step 2: Calculate the class midpoints. The class midpoint is the average of the lower and upper boundaries of each class. For example, for the first class (0–99), the midpoint is calculated as (0 + 99) / 2 = 49.5. Repeat this calculation for all classes.
3. Step 3: Determine the class boundaries. The class boundaries are the values that separate one class from another without gaps. For example, the boundary between the first class (0–99) and the second class (100–199) is 99.5. Add 0.5 to the upper limit of each class and subtract 0.5 from the lower limit of each class to find all boundaries.
4. Step 4: Calculate the total number of individuals included in the summary. Add up all the frequencies provided in the table. For example, 1 + 51 + 90 + 10 + 0 + 0 + 1 = Total individuals.
5. Step 5: Verify the calculations and ensure all values (class width, midpoints, boundaries, and total individuals) are consistent with the frequency distribution provided in the table.

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 0-99, the class width is 99 - 0 = 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 that interval. For instance, for the class 100-199, the midpoint is (100 + 199) / 2 = 149.5. Class midpoints are useful for summarizing data and performing further statistical analysis, such as calculating the mean.

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 0-99 and 100-199 would be 99.5. Class boundaries help in accurately representing continuous data and avoiding gaps between classes.