https://file.aiquickdraw.com/mathbot/file/1730266521361h6pfzae9.jpg

Let's go through each part of the question:

1. **Class Width (a):**
   The class width is the difference between the lower boundaries of consecutive classes. In this case:
   - \( 53 - 50 = 3 \)
   Therefore, the class width is **3**.

2. **Class Midpoints of the First Class (b):**
   The midpoint of a class is calculated by taking the average of the lower and upper limits of that class.
   - For the first class (50 - 52), the midpoint is \( \frac{50 + 52}{2} = 51 \).
   So, the class midpoint of the first class is **51**.

3. **Class Boundaries of the First Class (c):**
   Class boundaries are calculated by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit.
   - For the first class (50 - 52), the boundaries are:
     - Lower boundary: \( 50 - 0.5 = 49.5 \)
     - Upper boundary: \( 52 + 0.5 = 52.5 \)
   Therefore, the class boundaries for the first class are **49.5 - 52.5**.

Now let's match these with the options provided:

- The correct answer is **Option B**: \( \text{(a) 3 | (b) 51 | (c) 49.5-52.5} \).

Would you like more details or have any questions?

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Here are some related questions for practice:

1. How do you calculate the frequency density of a class in a frequency distribution?
2. What are class intervals, and why are they important in grouped data?
3. How can you determine the total number of data points from a frequency distribution?
4. What would happen to the class width if we added another class from 65-67?
5. How does calculating class boundaries help when creating histograms?

**Tip:** Remember, class boundaries help avoid gaps between classes in continuous data, which is useful in graphical representations like histograms.

Use the given frequency distribution to find the (a) class width, (b) class midpoints of the first class, and (c) class boundaries of the first class. Options provided for selection.

Learn how to determine the class width, midpoints, and boundaries for a frequency distribution. This example uses a height dataset with classes such as 50-52 inches and demonstrates calculations suitable for students in Grades 9-10.

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