To find the class boundaries, midpoint, and class width for the class interval "53-61", we can follow these steps:

1. Class Boundaries:

   • Class boundaries are calculated by extending the class limits slightly to avoid gaps between classes.
   • To find the boundaries, subtract 0.5 from the lower limit and add 0.5 to the upper limit.
   • For the class 53-61:
     • Lower class boundary = $53 - 0.5 = 52.5$
     • Upper class boundary = $61 + 0.5 = 61.5$
     • So, the class boundaries are 52.5 - 61.5.

2. Class Midpoint:

   • The midpoint is the average of the lower and upper class limits.
   • Midpoint = $\frac{53 + 61}{2} = \frac{114}{2} = 57$.
   • So, the midpoint is 57.

3. Class Width:

   • The class width is the difference between the upper and lower class limits.
   • Class width = $61 - 53 = 8$.
   • So, the class width is 8.

Summary:

• Class Boundaries: 52.5 - 61.5
• Midpoint: 57
• Class Width: 8

Would you like any further details or have any questions about these calculations?

Here are some related questions to consider:

1. What are class limits, and how are they different from class boundaries?
2. How would the class width change if the class interval was 53-65?
3. Why is it important to calculate class boundaries in grouped data?
4. How would you calculate the midpoint for a class interval with decimal limits (e.g., 53.5-61.5)?
5. How are these concepts used in creating histograms or frequency distributions?

Tip: Always calculate class boundaries when dealing with grouped data to prevent overlaps between consecutive classes.