To construct a grouped frequency distribution table (GFDT) for the given data set with 10 classes, let's go through the steps:

1. Identify the Range of Data:

   • Find the minimum and maximum values in the data set.
   • The minimum is $182$ and the maximum is $372$.
   • So, the range is $372 - 182 = 190$.

2. Determine Class Width:

   • We need 10 classes, so divide the range by the number of classes: $\text{Class Width} = \frac{190}{10} = 19$
   • Rounding up for simplicity, use a class width of $20$ (a "nice" number and multiple of 10).

3. Construct the Classes:

   • Starting from the minimum value $182$, create intervals of width $20$ each.
   • Each interval will be closed on the left and open on the right (e.g., $[182, 202)$).

4. Count Frequencies for Each Interval:

   • Count how many data points fall within each interval.

Let's organize this into a table. I'll calculate and display the frequencies for each interval accordingly.I've constructed the grouped frequency distribution table for the data set, displaying it with intervals and frequencies as specified. Each class has a width of 20, following the guidelines provided.

Would you like further details or have any questions?

Here are some related questions you might find helpful:

1. How can I calculate cumulative frequencies for this table?
2. What are some common ways to visualize a frequency distribution?
3. How do I determine the relative frequency for each class?
4. How do you interpret a grouped frequency distribution table?
5. What are the advantages of using grouped data versus raw data?

Tip: Always ensure your class intervals are non-overlapping and cover the entire range of your data for clarity in frequency distribution tables.