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: Identify the number of students and their scores
We know that there are 10 students in total. Among them:
- 3 students scored less than 30 marks.
- 3 students scored more than 75 marks.
- The scores of the remaining 4 students are 35, 40, 48, and 66.

### Step 2: List the scores in ascending order
To find the median, we need to arrange all the scores in ascending order. We can denote the scores of the students who scored less than 30 as "X" (where X < 30) and the scores of the students who scored more than 75 as "Y" (where Y > 75).

Thus, the scores can be represented as:
- Less than 30: X1, X2, X3
- Remaining scores: 35, 40, 48, 66
- More than 75: Y1, Y2, Y3

### Step 3: Arrange the scores
Since we don't know the exact scores of X1, X2, X3, Y1, Y2, Y3, we can assume:
- X1, X2, X3 < 30 (let's say they are the lowest scores)
- 35, 40, 48, 66 are the next scores
- Y1, Y2, Y3 > 75 (let's say they are the highest scores)

Thus, the complete arrangement in ascending order will look like this:
- X1, X2, X3, 35, 40, 48, 66, Y1, Y2, Y3

### Step 4: Determine the median position
Since the total number of students (n) is 10, which is even, the median is calculated using the formula:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]
Here, n = 10, so:
\[ \text{Median} = \frac{\text{5th term} + \text{6th term}}{2} \]

### Step 5: Identify the 5th and 6th terms
From our ordered list:
- The 5th term is 40
- The 6th term is 48

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

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

---