Find the class boundaries, midpoints, and widths for each class. 1.58-62 2.125-131 3. 16.35-18.46 4. 16.3-18.5
The Correct Answer and Explanation is :
To analyze the given classes, we will calculate the class boundaries, midpoints, and widths for each class.
Class 1: 1.58 – 62
- Class Boundaries: To find the boundaries, we subtract 0.01 from the lower limit and add 0.01 to the upper limit. Therefore, the class boundaries are:
- Lower boundary: 1.58 – 0.01 = 1.57
- Upper boundary: 62 + 0.01 = 62.01
- Boundaries: 1.57 – 62.01
- Midpoint: The midpoint is calculated by averaging the lower and upper limits:
- Midpoint = (1.58 + 62) / 2 = 31.79
- Width: The width is the difference between the upper and lower limits:
- Width = 62 – 1.58 = 60.42
Class 2: 2.125 – 131
- Class Boundaries:
- Lower boundary: 2.125 – 0.01 = 2.115
- Upper boundary: 131 + 0.01 = 131.01
- Boundaries: 2.115 – 131.01
- Midpoint:
- Midpoint = (2.125 + 131) / 2 = 66.0625
- Width:
- Width = 131 – 2.125 = 128.875
Class 3: 16.35 – 18.46
- Class Boundaries:
- Lower boundary: 16.35 – 0.01 = 16.34
- Upper boundary: 18.46 + 0.01 = 18.47
- Boundaries: 16.34 – 18.47
- Midpoint:
- Midpoint = (16.35 + 18.46) / 2 = 17.405
- Width:
- Width = 18.46 – 16.35 = 2.11
Class 4: 16.3 – 18.5
- Class Boundaries:
- Lower boundary: 16.3 – 0.01 = 16.29
- Upper boundary: 18.5 + 0.01 = 18.51
- Boundaries: 16.29 – 18.51
- Midpoint:
- Midpoint = (16.3 + 18.5) / 2 = 17.4
- Width:
- Width = 18.5 – 16.3 = 2.2
Summary Table
| Class | Boundaries | Midpoint | Width |
|---|---|---|---|
| 1.58 – 62 | 1.57 – 62.01 | 31.79 | 60.42 |
| 2.125 – 131 | 2.115 – 131.01 | 66.0625 | 128.875 |
| 16.35 – 18.46 | 16.34 – 18.47 | 17.405 | 2.11 |
| 16.3 – 18.5 | 16.29 – 18.51 | 17.4 | 2.2 |
Explanation
The class boundaries provide a range that accounts for all possible values that fall into a specific class by including the decimal points. The midpoints give us an average value that represents each class, useful for summarizing data. The width of each class indicates the range of values covered by the class, essential for determining how to group data for analysis. Understanding these components is vital in statistics for effective data organization and interpretation.