The median class in the following frequency distribution is
`{:("Class interval :",0-10,10-20,20-30,30-40,40-50),("Frequency :",12,13,25,20,10):}`

Options

A. `10-20`
B. `20-30`
C. `30-40`
D. none of these

Explanation

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

### Step 1: Calculate the Total Frequency (N)
We need to sum all the frequencies provided in the distribution.

- Frequencies: 12, 13, 25, 20, 10
- Total Frequency (N) = 12 + 13 + 25 + 20 + 10

Calculating this:
- 12 + 13 = 25
- 25 + 25 = 50
- 50 + 20 = 70
- 70 + 10 = 80

So, **N = 80**.

### Step 2: Calculate N/2
Now, we need to find N/2 to determine the median class.

- N/2 = 80/2 = 40

### Step 3: Calculate Cumulative Frequencies (CF)
Next, we will calculate the cumulative frequency for each class interval.

- For the class interval 0-10: CF = 12
- For the class interval 10-20: CF = 12 + 13 = 25
- For the class interval 20-30: CF = 25 + 25 = 50
- For the class interval 30-40: CF = 50 + 20 = 70
- For the class interval 40-50: CF = 70 + 10 = 80

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

### Step 4: Identify the Median Class
Now, we need to find the class interval where the cumulative frequency is just greater than N/2 (which is 40).

Looking at the cumulative frequencies:
- 12 (for 0-10) is less than 40
- 25 (for 10-20) is less than 40
- 50 (for 20-30) is greater than 40

Thus, the cumulative frequency that is just greater than 40 is 50, which corresponds to the class interval **20-30**.

### Conclusion
Therefore, the median class is **20-30**.

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