Out of 10 students, who appeared in a test, three secured less than 30 marks and 3 secured more than 75 marks. The marks secured by the remaining 4 students are 35, 48, 66 and 40. Find the median score of the whole group.

Answer

To find the median score of the group of 10 students, we will follow these steps:

### Step 1: List the scores of all students
We know that:
- 3 students scored less than 30 marks (let's assume they scored 20, 25, and 28 for calculation purposes).
- 3 students scored more than 75 marks (let's assume they scored 80, 85, and 90 for calculation purposes).
- The remaining 4 students scored 35, 48, 66, and 40.

So, the scores of all 10 students are:
- 20, 25, 28 (less than 30)
- 35, 40, 48, 66 (given scores)
- 80, 85, 90 (more than 75)

### Step 2: Arrange the scores in ascending order
Now, we will arrange all the scores in ascending order:
- 20, 25, 28, 35, 40, 48, 66, 80, 85, 90

### Step 3: Determine the number of scores
The total number of scores (n) is 10.

### Step 4: Find the median
Since the number of scores is even (n = 10), the median is calculated as the average of the 5th and 6th scores in the ordered list.

From our ordered list:
- The 5th score is 40.
- The 6th score is 48.

### Step 5: Calculate the median
Now, we calculate the median:
\[ \text{Median} = \frac{\text{5th score} + \text{6th score}}{2} = \frac{40 + 48}{2} = \frac{88}{2} = 44 \]

### Final Answer
The median score of the whole group is **44**.

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