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The image contains a frequency distribution table with cumulative frequencies (C.F.) and the median calculation using the formula for grouped data. Here's a breakdown of the steps:

### Given Data:

| Age   | No. of Persons | C.F.      |
|-------|----------------|-----------|
| 0-10  | 5              | 5         |
| 10-20 | 25             | 30        |
| 20-30 | \( x \)        | \( 30 + x \) |
| 30-40 | 18             | \( 48 + x \) |
| 40-50 | 7              | \( 55 + x \) |

- Total \( N = 55 + x \).
- Median is 24, which corresponds to the class interval \( 20-30 \).

### Formula for Median:
\[
\text{Median} = L + \left( \frac{N}{2} - C.F.\right) \times \frac{h}{f}
\]
Where:
- \( L = 20 \) (Lower boundary of the median class),
- \( N = 55 + x \) (Total frequency),
- \( C.F. = 30 \) (Cumulative frequency before the median class),
- \( h = 10 \) (Class width),
- \( f = x \) (Frequency of the median class).

### Median Calculation:
Using the formula:
\[
24 = 20 + \left( \frac{55 + x}{2} - 30 \right) \times \frac{10}{x}
\]

Simplify and solve for \( x \).

Let me calculate that.The value of \( x \) is 25. Therefore, the frequency of the 20-30 age group is 25.

Would you like further details on the steps or any clarifications?

Here are five related questions for further practice:
1. What would happen to the median if the value of \( x \) were different?
2. How do you calculate the mean from a frequency distribution like this one?
3. What if you were asked to calculate the mode instead of the median?
4. How would you compute the quartiles from this data?
5. How would you adjust the class intervals if the number of persons changed?

**Tip:** Always check if the total cumulative frequency \( N \) is consistent with the sum of individual frequencies for accuracy.

The median is 24, and the frequency distribution table is given. Find the missing frequency (x) using the median formula.

This problem involves calculating the missing frequency (x) from a frequency distribution table where the median is given as 24. It requires the use of the median formula for grouped data, where L = 20, N = 55 + x, C.F. = 30, and h = 10.

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