To answer the questions based on the provided table, let's go step by step.

The key points for solving histogram questions are:

1. Widest Bar: The width of a class in a histogram is determined by the range of the class interval.
2. Tallest Bar: The height of a bar in a histogram is determined by the frequency density, which is calculated as: $\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}$ where Class Width is the difference between the upper and lower bounds of the class.

Table:

a) Widest Class (Widest Bar)

The width of each class is the difference between the upper and lower bounds:

• For $50 < v \leq 54$: Class width = $54 - 50 = 4$
• For $54 < v \leq 56$: Class width = $56 - 54 = 2$
• For $56 < v \leq 59$: Class width = $59 - 56 = 3$
• For $59 < v \leq 67$: Class width = $67 - 59 = 8$
• For $67 < v \leq 72$: Class width = $72 - 67 = 5$

Answer: The widest class is $59 < v \leq 67$, with a width of 8.

b) Tallest Bar (Largest Frequency Density)

Now let's calculate the frequency density for each class:

• For $50 < v \leq 54$: $\text{Frequency Density} = \frac{10}{4} = 2.5$
• For $54 < v \leq 56$: $\text{Frequency Density} = \frac{15}{2} = 7.5$
• For $56 < v \leq 59$: $\text{Frequency Density} = \frac{24}{3} = 8$
• For $59 < v \leq 67$: $\text{Frequency Density} = \frac{28}{8} = 3.5$
• For $67 < v \leq 72$: $\text{Frequency Density} = \frac{39}{5} = 7.8$

Answer: The class with the tallest bar is $56 < v \leq 59$, with a frequency density of 8.

Would you like further clarification on any part of this solution? Here are five related questions you might find helpful:

1. How does frequency density relate to histograms?
2. Can a class with a higher frequency have a shorter bar than a lower-frequency class?
3. How would you interpret a histogram visually based on this data?
4. What does a wider bar represent in a histogram compared to a taller bar?
5. Could you explain how to find the total number of observations from the data?

Tip: When working with histograms, always double-check the class widths since they are essential for calculating the correct bar heights (frequency density).