Could you explain how to calculate the class center and class boundaries for a frequency distribution table?

The table shows:

• Class limits: The range of values for each class (e.g., $30-39$).
• Frequency: The number of data points falling within that class (e.g., 5).
• Class boundaries: The exact limits used for drawing a histogram, ensuring no gaps between bars.
• Class center (or midpoint): The middle value of the class interval.

The class center is calculated as the average of the lower and upper class limits.
For the class $30-39$:

$$\text{Class Center} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$$ $$\text{Class Center} = \frac{30 + 39}{2} = \frac{69}{2} = 34.5$$

Your handwritten calculation $\frac{30+39}{2} = 34.5$ is correct.

Class boundaries are found by subtracting 0.5 from the lower class limit and adding 0.5 to the upper class limit to create continuous intervals.
For the class $30-39$:

$$\text{Lower Class Boundary} = 30 - 0.5 = 29.5$$ $$\text{Upper Class Boundary} = 39 + 0.5 = 39.5$$

The class boundaries $29.5-39.5$ are correctly derived.

The visible data and your calculation are accurate for the given class interval. To draw a complete histogram, you would need all class intervals and their corresponding frequencies.