To construct a frequency distribution with 5 classes, we first need to determine the class width, the class limits, and then count the frequency of the data points that fall within each class.

Steps to create the frequency distribution:

1. Find the range of the data:

   • The lowest value is $0$ and the highest value is $19$.
   • Range = Highest value - Lowest value = $19 - 0 = 19$

2. Determine the class width:

   • Class width = $\frac{\text{Range}}{\text{Number of classes}}$
   • $\frac{19}{5} \approx 3.8$, but we round up to 4 to make the class limits easier to manage.

3. Determine the class limits:

   • Starting with the lowest class limit (0), add the class width to determine the subsequent upper class limits.
   • Class 1: 0 - 3
   • Class 2: 4 - 7
   • Class 3: 8 - 11
   • Class 4: 12 - 15
   • Class 5: 16 - 19

4. Count the frequency for each class:

   • Class 1 (0 - 3): 0, 1, 2, 2, 2 → Frequency = 5
   • Class 2 (4 - 7): 4, 4, 7 → Frequency = 3
   • Class 3 (8 - 11): 8, 9, 11, 11 → Frequency = 4
   • Class 4 (12 - 15): 12, 14 → Frequency = 2
   • Class 5 (16 - 19): 16, 18, 18, 19, 19, 19 → Frequency = 6

Frequency Distribution Table:

Would you like a more detailed explanation or have any questions?

Here are some related questions:

1. How do you calculate the midpoint of each class?
2. What is the purpose of constructing a frequency distribution?
3. How do you determine the cumulative frequency for each class?
4. How would the frequency distribution change if you used 10 classes instead of 5?
5. What are the benefits of rounding up the class width?
6. How can you create a histogram based on this frequency distribution?
7. What is the difference between relative frequency and frequency?
8. How would you calculate the relative frequency for each class?

Tip: When constructing frequency distributions, always round up the class width to ensure that all data points are included and no gaps are left between classes.