Ages	Number of students
15-18	2
19-22	4
23-26	8
27-30	9
31-34	6
35-38	3

Based on the frequency distribution above, is 22.5 a:
Class midpoint
Upper class limit
Lower class limit
Class boundary
Class width

Given the frequency distribution and the possible options, let's analyze where 22.5 fits:

1. **Class Midpoint**: The midpoint of a class is calculated by averaging the lower and upper limits of the class. For the class "19-22":
   \[
   \text{Midpoint} = \frac{19 + 22}{2} = \frac{41}{2} = 20.5
   \]
   For the class "23-26":
   \[
   \text{Midpoint} = \frac{23 + 26}{2} = \frac{49}{2} = 24.5
   \]
   So, 22.5 is not a class midpoint.

2. **Upper Class Limit**: This is the highest value that can be included in a class interval. For the class "19-22", the upper class limit is 22. So, 22.5 is not an upper class limit.

3. **Lower Class Limit**: This is the lowest value that can be included in a class interval. For the class "23-26", the lower class limit is 23. So, 22.5 is not a lower class limit.

4. **Class Boundary**: Class boundaries are used to separate classes so there are no gaps between them. The boundary between the "19-22" and "23-26" classes is:
   \[
   \text{Boundary} = \frac{22 + 23}{2} = 22.5
   \]
   So, 22.5 **is** a class boundary.

5. **Class Width**: This is the difference between the upper and lower limits of a class. For "19-22", the width is:
   \[
   \text{Width} = 22 - 19 = 3
   \]
   So, 22.5 is not a class width.

**Conclusion:** 22.5 is a **class boundary**.

Would you like more details or have any questions? 

Here are 5 related questions:
1. How is the class midpoint calculated for a frequency distribution?
2. What is the significance of class boundaries in frequency distributions?
3. How do you determine the class width from a given frequency distribution?
4. What is the difference between a class limit and a class boundary?
5. How do you interpret frequency distributions in terms of data analysis?

**Tip:** Class boundaries are especially important when you're dealing with continuous data, as they help to eliminate gaps between classes.

Based on the frequency distribution above, is 22.5 a: Class midpoint, Upper class limit, Lower class limit, Class boundary, or Class width?

Analyze whether 22.5 is a class midpoint, class boundary, or class limit based on the provided frequency distribution. This problem covers essential statistical concepts, including class boundaries, class widths, and class midpoints. Suitable for high school students in Grades 10-12.

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