Marks scored by 100 students in a 25 marks unit test of Mathematics is given below. Their median is
`{:("Marks " ,0-5,5-10,10-15,15-20,20-25),("Students "," "10," "18," "42," "23," "7):}`

Options

A. 12
B. `12.63`
C. `12.3`
D. `12.7`

Answer

To find the median of the marks scored by 100 students in a 25 marks unit test of Mathematics, we will follow these steps:

### Step 1: Create a frequency distribution table
We will organize the given data into a frequency distribution table.

| Marks | Students (Frequency) |
|-------------|----------------------|
| 0 - 5 | 10 |
| 5 - 10 | 18 |
| 10 - 15 | 42 |
| 15 - 20 | 23 |
| 20 - 25 | 7 |
| **Total** | **100** |

### Step 2: Calculate cumulative frequency
Next, we will calculate the cumulative frequency (CF) for the frequency distribution.

| Marks | Students (Frequency) | Cumulative Frequency (CF) |
|-------------|----------------------|---------------------------|
| 0 - 5 | 10 | 10 |
| 5 - 10 | 18 | 28 |
| 10 - 15 | 42 | 70 |
| 15 - 20 | 23 | 93 |
| 20 - 25 | 7 | 100 |

### Step 3: Find \( n/2 \)
Since there are 100 students, we calculate \( n/2 \):
\[ n/2 = 100/2 = 50 \]

### Step 4: Identify the median class
From the cumulative frequency table, we find the class interval where the cumulative frequency is just greater than or equal to 50. The cumulative frequency of 70 (for the class 10 - 15) is the first one that exceeds 50. Thus, the median class is 10 - 15.

### Step 5: Identify the values needed for the median formula
- **L** (lower limit of the median class) = 10
- **CF** (cumulative frequency of the class before the median class) = 28 (for the class 5 - 10)
- **f** (frequency of the median class) = 42
- **h** (class width) = 5 (since 10 - 15 = 5)

### Step 6: Apply the median formula
The formula for the median is given by:
\[ \text{Median} = L + \left( \frac{n/2 - CF}{f} \right) \times h \]
Substituting the values we have:
\[ \text{Median} = 10 + \left( \frac{50 - 28}{42} \right) \times 5 \]
\[ = 10 + \left( \frac{22}{42} \right) \times 5 \]
\[ = 10 + \left( \frac{110}{42} \right) \]
\[ = 10 + 2.619 \]
\[ = 12.619 \approx 12.63 \]

### Conclusion
Thus, the median marks scored by the students is approximately **12.63**.