https://file.aiquickdraw.com/mathbot/file/1728930173101tj5id2hg.jpg

Let's break down the question based on the frequency distribution table in the image.

### 1. Class Width
The class width is the difference between the lower limits of two consecutive classes. We can calculate it by subtracting the lower limit of one class from the lower limit of the next class.

For example:
\[
\text{Class Width} = 68.0 - 64.0 = 4.0 \text{ inches}
\]

### 2. Class Midpoints
The class midpoint is the average of the lower and upper limits of each class. The formula for the midpoint is:
\[
\text{Class Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}
\]

Let's calculate them:
- For the first class (64.0–67.9): 
  \[
  \text{Midpoint} = \frac{64.0 + 67.9}{2} = 65.95
  \]
- For the second class (68.0–71.9): 
  \[
  \text{Midpoint} = \frac{68.0 + 71.9}{2} = 69.95
  \]
- For the third class (72.0–75.9): 
  \[
  \text{Midpoint} = \frac{72.0 + 75.9}{2} = 73.95
  \]
- And similarly for the remaining classes.

### 3. Class Boundaries
Class boundaries are used to avoid gaps between classes. The lower class boundary is the smallest value that belongs to the class, while the upper class boundary is the largest value that belongs to the class. To find the class boundaries, we subtract 0.05 from the lower limit and add 0.05 to the upper limit.

For example:
- For the first class (64.0–67.9):
  \[
  \text{Lower Boundary} = 64.0 - 0.05 = 63.95, \quad \text{Upper Boundary} = 67.9 + 0.05 = 67.95
  \]

Thus, the class boundaries for the first class are 63.95–67.95.

Would you like detailed calculations for all class midpoints and boundaries?

Here are some related questions that expand on this information:

1. How do you calculate class midpoints for grouped data?
2. Why are class boundaries important in frequency distributions?
3. How do you calculate class width if the intervals aren't consistent?
4. What are the advantages of using class midpoints in statistics?
5. How do frequency distributions help in understanding data?

**Tip:** When calculating class width, make sure the intervals are uniform across the distribution; otherwise, adjust your calculations accordingly.

Identify the class width, class midpoints, and class boundaries for the given frequency distribution.

Learn how to calculate the class width, class midpoints, and class boundaries for a given frequency distribution. Detailed step-by-step instructions are provided along with examples from a height distribution dataset. Suitable for high school students in Grades 9-12.

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