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Let's walk through the steps needed to determine the **median hours of work** from the provided data.

### Data extracted:
- **Hours/Week**: 19, 26, 22, 8, 12, 3, 2  
- **Frequency**: 16, 14, 14, 12, 11, 10, 4  

The **median** is the middle value when all observations are arranged in **ascending order**. Since the data is given in grouped form (hours along with their frequencies), we first need to create a cumulative frequency table to locate the **median position**.

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### Step 1: Arrange data and cumulative frequency  
We'll first arrange the hours in **increasing order**:

| Hours/Week | Frequency | Cumulative Frequency |
|------------|-----------|----------------------|
| 2          | 4         | 4                    |
| 3          | 10        | 14                   |
| 8          | 12        | 26                   |
| 12         | 11        | 37                   |
| 19         | 16        | 53                   |
| 22         | 14        | 67                   |
| 26         | 14        | 81                   |

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### Step 2: Find the total frequency  
- Total frequency (n) = 81 students

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### Step 3: Locate the median position  
- **Median position** = \( \frac{n + 1}{2} = \frac{81 + 1}{2} = \frac{82}{2} = 41 \)  
The **41st observation** will be the median.

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### Step 4: Identify the median class  
From the cumulative frequency table, we can see that:
- The **37th observation** is in the 12-hour group.
- The **41st observation** will fall in the **19-hour group** (since cumulative frequency reaches 53 at this group).

---

### Step 5: Conclusion  
Thus, the **median hours of work** is **19 hours per week**.

---

Do you have any questions or want me to break this down further?

### 5 Related Questions:
1. How is the cumulative frequency helpful in finding the median?
2. What if the frequencies were even—how would that affect the median?
3. How would you find the mode for this dataset?
4. What is the difference between mean, median, and mode?
5. How can this method be extended to larger datasets?

**Tip:** When working with frequency data, always ensure cumulative frequency is correctly calculated to avoid mistakes in locating the median.

The following is a list from a random survey at a university asking students how many hours per week they work either on or off campus at their job. Determine the median hours of work.

Learn how to find the median hours of work using a random survey dataset with frequency distributions. The solution includes calculating cumulative frequency and locating the median position.

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