Find the median of the following data.
`{:("Class Interval",f),(" "0-10,12),(" "10-20,13),(" "20-30,25),(" "30-40,20),(" "40-50,10):}`

Options

A. 25
B. 23
C. 24
D. 26

Explanation

To find the median of the given frequency distribution, we will follow these steps:

### Step 1: Create a Cumulative Frequency Table
First, we need to create a cumulative frequency table based on the given data.

| Class Interval | Frequency (f) | Cumulative Frequency (CF) |
|----------------|---------------|---------------------------|
| 0 - 10 | 12 | 12 |
| 10 - 20 | 13 | 12 + 13 = 25 |
| 20 - 30 | 25 | 25 + 25 = 50 |
| 30 - 40 | 20 | 50 + 20 = 70 |
| 40 - 50 | 10 | 70 + 10 = 80 |

So, the cumulative frequencies are:
- For 0-10: 12
- For 10-20: 25
- For 20-30: 50
- For 30-40: 70
- For 40-50: 80

### Step 2: Calculate N and N/2
Next, we calculate N (the total frequency) and N/2:
- N = 80 (sum of all frequencies)
- N/2 = 80 / 2 = 40

### Step 3: Identify the Median Class
Now, we need to find the median class. The median class is the class interval where the cumulative frequency is just greater than N/2 (40).

From our cumulative frequency table:
- The cumulative frequency just greater than 40 is 50, which corresponds to the class interval 20-30.

Thus, the median class is 20-30.

### Step 4: Identify L, CF, F, and H
Now we need to identify:
- L (lower limit of the median class) = 20
- CF (cumulative frequency of the class before the median class) = 25 (for the class 10-20)
- F (frequency of the median class) = 25 (for the class 20-30)
- H (width of the class interval) = 30 - 20 = 10

### Step 5: Apply the Median Formula
Now we can use the median formula:
\[ \text{Median} = L + \left(\frac{N/2 - CF}{F}\right) \times H \]

Substituting the values:
\[ \text{Median} = 20 + \left(\frac{40 - 25}{25}\right) \times 10 \]
\[ = 20 + \left(\frac{15}{25}\right) \times 10 \]
\[ = 20 + 0.6 \times 10 \]
\[ = 20 + 6 \]
\[ = 26 \]

### Final Answer
The median of the given data is **26**.

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