Answer :
To find the class boundaries, midpoint, and width for the class range 31.3-36.9, let's break down the steps needed to solve this. We'll choose the correct answer from the options provided after explaining each step.
Class Boundaries:
Class boundaries are calculated by subtracting and adding 0.05 (half of the smallest unit in the data) to the lower and upper class limits respectively. This adjustment accounts for the coverage of continuous data.
- Lower Class Boundary: [tex]31.3 - 0.05 = 31.25[/tex]
- Upper Class Boundary: [tex]36.9 + 0.05 = 36.95[/tex]
Therefore, the class boundaries are 31.25-36.95.
Midpoint:
The midpoint of a class is found by averaging the lower and upper class limits. This gives the central value of the class range.
- Midpoint: [tex]\frac{31.3 + 36.9}{2} = 34.1[/tex]
Width:
The class width is calculated by subtracting the lower class boundary from the upper class boundary.
- Width: [tex]36.95 - 31.25 = 5.7[/tex]
Now that we've calculated each component, let's match them with the provided options:
- Option 1: Boundaries: 31.3-36.9, midpoint: 34.1, width: 5.6
- Option 2: Boundaries: 31.25-36.95, midpoint: 34.6, width: 5.7
- Option 3: Boundaries: 31.25-36.95, midpoint: 34.1, width: 5.7
- Option 4: Boundaries: 31.25-36.95, midpoint: 34.1, width: 5.6
The correct option is Option 3: Boundaries: 31.25-36.95, midpoint: 34.1, width: 5.7.