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To solve this problem, we need to determine the lower boundary of the median group from the frequency table provided. Here’s how we can approach it:

### Step 1: Calculate the cumulative frequency
We first calculate the cumulative frequency, which will help us find the median class.

| Age Group | Frequency (f) | Cumulative Frequency (cf) |
|-----------|---------------|---------------------------|
| 18 - 26   | 3             | 3                         |
| 27 - 35   | 5             | 8                         |
| 36 - 44   | 9             | 17                        |
| 45 - 53   | 14            | 31                        |
| 54 - 62   | 11            | 42                        |
| 63 - 71   | 6             | 48                        |
| 72 - 80   | 2             | 50                        |

### Step 2: Locate the median class
Since there are 50 observations, the median is the 25th observation (because \( \frac{50 + 1}{2} = 25.5 \)).

From the cumulative frequency, we see that the 25th observation falls in the class interval **45 - 53** (since its cumulative frequency is 31).

### Step 3: Lower boundary of the median class
The lower boundary of the age group 45 - 53 is **44.5**. (The lower boundary is typically found by subtracting 0.5 from the lower limit of the class.)

Thus, the **lower boundary of the median group** is **44.5**.

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Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. How do you calculate the exact value of the median for a grouped frequency distribution?
2. What is the formula for determining the median class in a frequency distribution?
3. Why is the lower boundary adjusted by subtracting 0.5?
4. How can you calculate the mean age from the same frequency table?
5. What would happen if the total number of customers was odd instead of even?

**Tip:** In frequency distributions, the median class is identified using cumulative frequencies to find where the middle value lies.

What is the lower boundary of the median group of people taking travel?

Learn how to find the lower boundary of the median group from a frequency distribution table. This step-by-step solution uses cumulative frequency and explains how to calculate the median for a group of 50 observations. Suitable for high school students studying statistics.

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