To determine the number of classes in the frequency histogram, we need to count the distinct intervals or bars (often referred to as "bins" or "classes") that represent the data.

In this case, the x-axis values (63, 66, 69, ..., 96) likely represent the endpoints of the classes (intervals). The difference between successive x-values is 3, which suggests that each class spans a 3-point range.

The x-axis values start at 63 and end at 96. We can count the number of intervals (classes) by calculating how many times 3 fits into the range from 63 to 96.

1. First, find the total number of classes by using the formula: $\text{Number of classes} = \frac{\text{Upper endpoint} - \text{Lower endpoint}}{\text{Class width}} + 1$ Here:

   • Upper endpoint = 96
   • Lower endpoint = 63
   • Class width = 3

2. Plug in the values: $\text{Number of classes} = \frac{96 - 63}{3} + 1 = \frac{33}{3} + 1 = 11 + 1 = 12$

Therefore, there are 12 classes in this histogram.

Would you like further details on how these classes work or any other questions?

Here are 5 related questions to expand on this topic:

1. What is the importance of class width in a histogram?
2. How do you calculate the frequency density of each class?
3. How would you calculate the mean final grade from this histogram?
4. What does the shape of this histogram suggest about the distribution of grades?
5. How can you determine the mode from this frequency histogram?

Tip: Always ensure that the class width is consistent across all intervals in a histogram for accurate data representation.