The marks of Eleven students in ascending order for a test are given below with Median as 36, the value of k is : 10, 12, 16, 25, 28, k+3, k+5, 43, 45, 47, 53

Options

A. 36
B. 37
C. 35
D. 33

Answer

To solve the problem of finding the value of \( k \) given the marks of eleven students and the median, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
The marks of the eleven students in ascending order are:
\[ 10, 12, 16, 25, 28, k+3, k+5, 43, 45, 47, 53 \]
We are also given that the median of these marks is 36.

2. **Understand the Concept of Median**:
The median is the middle value of a data set. For an odd number of observations, the median is the value at the position \(\frac{n+1}{2}\), where \( n \) is the number of observations. Here, \( n = 11 \).

3. **Calculate the Position of the Median**:
Since \( n = 11 \):
\[ \text{Position of Median} = \frac{11 + 1}{2} = 6 \]
This means the median is the 6th term in the ordered list.

4. **Identify the 6th Term**:
From the ordered list, the 6th term is \( k + 3 \).

5. **Set Up the Equation**:
Since we know that the median is 36, we can set up the equation:
\[ k + 3 = 36 \]

6. **Solve for \( k \)**:
To find \( k \), we subtract 3 from both sides:
\[ k = 36 - 3 \]
\[ k = 33 \]

### Conclusion:
The value of \( k \) is \( 33 \).