The image shows a dataset and a task to construct a grouped frequency distribution table (GFDT) with 10 classes, following specific rules for class width and interval notation. Let’s walk through how to solve this step-by-step.

Steps to Solve

1. Determine the range of the data:

   • The smallest value in the dataset is 53.
   • The largest value in the dataset is 297.
   • The range is:
     $\text{Range} = \text{Max} - \text{Min} = 297 - 53 = 244$

2. Calculate the class width:

   • You want 10 classes, so the class width is:
     $\text{Class Width} = \lceil \frac{\text{Range}}{\text{Number of Classes}} \rceil = \lceil \frac{244}{10} \rceil = 25$

3. Create class intervals:

   • The lower boundary of the first class is the smallest data value (53).
   • Each class spans 25 units.
   • The intervals are:
     $[53, 77), [77, 102), [102, 127), [127, 152), [152, 177), [177, 202), [202, 227), [227, 252), [252, 277), [277, 302)$
   • Note: These intervals use closed on the lower end and open on the upper end (e.g., [53, 77)).

4. Count the frequencies:

   • Count how many data points fall into each interval. Here’s the breakdown:

Final Answer (Grouped Frequency Distribution Table)

Let me know if you'd like a further breakdown or have questions! 😊

5 Related Questions:

1. What is the purpose of a grouped frequency distribution table?
2. How do you decide on the number of classes in a GFDT?
3. Why is the class width rounded up when dividing the range?
4. How can you create a histogram based on the GFDT?
5. What are some common errors when constructing a GFDT?

Tip: Always double-check your class intervals to ensure they do not overlap and that all data points are included in the correct interval!