To construct the frequency table for the given data with 6 classes, we can follow these steps:

Step 1: Determine the Range

First, we need to find the range of the data:

• Maximum Value: 68
• Minimum Value: 15

Range = Maximum Value − Minimum Value = 68 − 15 = 53.

Step 2: Determine Class Width

Next, divide the range by the number of classes (6). The class width is approximately: $\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{53}{6} \approx 8.83$ Since the class width must be a whole number, we'll round it up to 9.

Step 3: Create the Classes

Starting from the minimum value (15), we will create 6 classes with a width of 9:

• Class 1: 15 - 23
• Class 2: 24 - 32
• Class 3: 33 - 41
• Class 4: 42 - 50
• Class 5: 51 - 59
• Class 6: 60 - 68

Step 4: Count the Frequencies

Now, we count how many data points fall into each class:

• Class 1 (15 - 23): 15, 17, 18, 19 → Frequency = 4
• Class 2 (24 - 32): 25, 25, 27, 28, 29, 30, 30, 32 → Frequency = 8
• Class 3 (33 - 41): 33, 36, 38 → Frequency = 3
• Class 4 (42 - 50): 45, 45, 48, 49, 50 → Frequency = 5
• Class 5 (51 - 59): 52, 53, 55, 56, 57, 58, 59, 59 → Frequency = 8
• Class 6 (60 - 68): 63, 68 → Frequency = 2

Step 5: Construct the Table

Lower Class Limit	Upper Class Limit	Frequency
15	23	4
24	32	8
33	41	3
42	50	5
51	59	8
60	68	2

Answer:

The frequency table for the given data is as follows:

Lower Class Limit	Upper Class Limit	Frequency
15	23	4
24	32	8
33	41	3
42	50	5
51	59	8
60	68	2

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Would you like further details or assistance with other aspects of this problem?

Here are some related questions for practice:

1. How would the frequency table change if we used a class width of 8 instead of 9?
2. What is the cumulative frequency for each class in the above table?
3. How do you determine the class boundaries for this frequency table?
4. How can you visualize this data using a histogram?
5. What is the mean age of the students based on the frequency table?

Tip: When constructing a frequency table, always round the class width to a convenient number that ensures all data points are included in the ranges.