The median of the following frequency distribution is
`{:("Class interval",f),(" "0-10,5),(" "10-20,8),(" "20-30,7),(" "30-40,10),(" "40-50,20):}`

Options

A. 35
B. 30
C. 40
D. 45

Explanation

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

### Step 1: Organize the Data
We have the following frequency distribution:

| Class Interval | Frequency (f) |
|----------------|---------------|
| 0 - 10 | 5 |
| 10 - 20 | 8 |
| 20 - 30 | 7 |
| 30 - 40 | 10 |
| 40 - 50 | 20 |

### Step 2: Calculate the Cumulative Frequency
We will calculate the cumulative frequency (cf) for each class interval.

- For 0 - 10: cf = 5
- For 10 - 20: cf = 5 + 8 = 13
- For 20 - 30: cf = 13 + 7 = 20
- For 30 - 40: cf = 20 + 10 = 30
- For 40 - 50: cf = 30 + 20 = 50

So, the cumulative frequency table is:

| Class Interval | Frequency (f) | Cumulative Frequency (cf) |
|----------------|---------------|----------------------------|
| 0 - 10 | 5 | 5 |
| 10 - 20 | 8 | 13 |
| 20 - 30 | 7 | 20 |
| 30 - 40 | 10 | 30 |
| 40 - 50 | 20 | 50 |

### Step 3: Determine Total Frequency (N)
Now, we will find the total frequency (N):

\[ N = 5 + 8 + 7 + 10 + 20 = 50 \]

### Step 4: Find \( n/2 \)
Next, we calculate \( n/2 \):

\[ n/2 = 50/2 = 25 \]

### Step 5: Identify the Median Class
We need to find the median class, which is the class interval where the cumulative frequency is greater than or equal to \( n/2 \).

From the cumulative frequency table:
- The cumulative frequency just before 25 is 20 (for the class 20 - 30).
- The cumulative frequency that is greater than or equal to 25 is 30 (for the class 30 - 40).

Thus, the median class is **30 - 40**.

### Step 6: Identify Values for the Median Formula
Now we can identify the values needed for the median formula:

- \( l \) (lower limit of median class) = 30
- \( cf \) (cumulative frequency of the class before median class) = 20
- \( f \) (frequency of median class) = 10
- \( h \) (class width) = 10 (since 40 - 30 = 10)

### Step 7: Apply the Median Formula
The formula for the median is:

\[ \text{Median} = l + \frac{n/2 - cf}{f} \times h \]

Substituting the values we have:

\[ \text{Median} = 30 + \frac{25 - 20}{10} \times 10 \]

Calculating this:

\[ \text{Median} = 30 + \frac{5}{10} \times 10 \]
\[ \text{Median} = 30 + 5 = 35 \]

### Final Answer
The median of the given frequency distribution is **35**.

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