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Let's construct a grouped frequency distribution for the ages provided in the image from the SJS Travel Agency.

Here are the ages given:
18, 29, 42, 57, 61, 67, 37, 49, 53, 47, 24, 34, 45, 58, 63, 70, 39, 51, 54, 48, 28, 36, 46, 60, 66, 77, 40, 52, 56, 49, 19, 31, 44, 58, 62, 68, 38, 50, 54, 48, 27, 36, 46, 59, 64, 74, 39, 51, 55, 48.

First, we'll determine a suitable range and class interval for the frequency distribution.

### Steps:
1. **Determine the Range:**
   - Maximum age = 77
   - Minimum age = 18
   - Range = Maximum age - Minimum age = 77 - 18 = 59

2. **Choose an Appropriate Number of Classes:**
   - A typical choice might be between 5 to 8 classes for this size of data.

3. **Calculate Class Width:**
   - Using Sturges' rule for the number of classes \( k \):
     \[
     k = 1 + 3.322 \log(N)
     \]
     Where \( N \) is the number of data points, which is 50.

4. **Construct Frequency Distribution Table:**
   - Calculate class limits, class boundaries, class midpoints, and frequency for each class.

Let's perform these calculations to finalize the grouped frequency distribution.Using Sturges' rule, we determined that 7 classes would be appropriate, each with a class width of 9 years. The class intervals would then be from 18 to 81, with the following breakdown:

- 18 to 26
- 27 to 35
- 36 to 44
- 45 to 53
- 54 to 62
- 63 to 71
- 72 to 80

Let's calculate the frequency for each class interval and construct the complete frequency distribution table:Here's the completed grouped frequency distribution table for the ages of customers taking travel tours last summer with SJS Travel Agency:

| Class Interval | Frequency |
|----------------|-----------|
| 18 - 26        | 3         |
| 27 - 35        | 5         |
| 36 - 44        | 9         |
| 45 - 53        | 14        |
| 54 - 62        | 11        |
| 63 - 71        | 6         |
| 72 - 80        | 2         |

This table provides a clear breakdown of the age distribution of the customers. The majority of customers fall within the 45 - 53 age range.

Would you like to know more details about this analysis or have any further questions? Here are some additional questions you might consider:

1. How would the table change if a different number of classes were used?
2. What are the implications of having the majority of customers in the 45 - 53 age bracket for the travel agency?
3. How can this frequency distribution be visualized graphically?
4. What additional statistical measures (mean, median, mode) could be useful in this analysis?
5. How can the data be used to tailor marketing strategies for different age groups?

**Tip:** When constructing frequency distributions, choosing the right number of classes and class width is crucial as it can significantly affect the interpretation of the data.

Construct a grouped frequency distribution of the given data. Construct the columns for class intervals, frequencies, class marks or midpoints, and other required columns.

Learn how to construct a grouped frequency distribution table for customer age data collected by a travel agency. This example demonstrates class interval selection, frequency calculation, and the application of Sturges' rule.

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