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The problem in the image appears to be asking for the **median** and **mode** of a frequency distribution based on daily wages and the number of persons. Here's the distribution presented in the table:

| **Daily Wages** | **Number of Persons** |
|-----------------|-----------------------|
| 5               | 7                     |
| 10              | 12                    |
| 15              | 16                    |
| 20              | 37                    |
| 25              | 22                    |
| 30              | 11                    |

### 1. **Mode**:
The mode is the daily wage that corresponds to the highest frequency of persons.

- The highest frequency in this case is 37 persons, which corresponds to a daily wage of **20**.

So, the **mode** of the distribution is **20**.

### 2. **Median**:
To find the median, we need to calculate the cumulative frequency and locate the middle value in the data.

#### Step 1: Calculate the Cumulative Frequency

| **Daily Wages** | **Number of Persons** | **Cumulative Frequency** |
|-----------------|-----------------------|--------------------------|
| 5               | 7                     | 7                        |
| 10              | 12                    | 7 + 12 = 19              |
| 15              | 16                    | 19 + 16 = 35             |
| 20              | 37                    | 35 + 37 = 72             |
| 25              | 22                    | 72 + 22 = 94             |
| 30              | 11                    | 94 + 11 = 105            |

#### Step 2: Find the Median Class
- The total number of persons is 105.
- The median is the value that corresponds to the \( \frac{105}{2} = 52.5 \)th person.

The cumulative frequency reaches 52.5 in the **20** wage class (cumulative frequency of 72). So, the median class is the one with daily wages of **20**.

#### Step 3: Apply the Median Formula
The median formula for grouped data is:

\[
\text{Median} = L + \left( \frac{\frac{N}{2} - F}{f} \right) \times h
\]

Where:
- \( L = 20 \) (lower boundary of the median class)
- \( N = 105 \) (total frequency)
- \( F = 35 \) (cumulative frequency of the class preceding the median class)
- \( f = 37 \) (frequency of the median class)
- \( h = 5 \) (class width)

Now, substituting the values:

\[
\text{Median} = 20 + \left( \frac{52.5 - 35}{37} \right) \times 5
\]
\[
\text{Median} = 20 + \left( \frac{17.5}{37} \right) \times 5
\]
\[
\text{Median} = 20 + \left( 0.473 \right) \times 5
\]
\[
\text{Median} \approx 20 + 2.37 = 22.37
\]

So, the **median** wage is approximately **22.37**.

---

Would you like to explore more details or have any further questions? Here are some additional problems you might be interested in:

1. How do you calculate the mean for this data set?
2. Can you calculate the range of daily wages for this distribution?
3. What is the variance and standard deviation of the daily wages?
4. How would the results change if the frequency distribution were grouped differently?
5. How does the mode compare to the median in different types of distributions?

**Tip:** When working with grouped data, always remember to check the class boundaries carefully to ensure accurate calculations.

Find the median and mode of the following distribution: Daily Wages (5, 10, 15, 20, 25, 30) and Number of Persons (7, 12, 16, 37, 22, 11).

This example explains how to calculate the median and mode for a frequency distribution based on daily wages and the number of persons. We use the cumulative frequency method to find the median and identify the mode as the wage with the highest frequency. Suitable for high school students in Grades 9-12.

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