Explanation:

- The marks obtained are in an arithmetic progression (AP).

- The first term of this AP is 4.

- The common difference of the AP is 3.

- The number of students, or total terms, is 51.

Steps:

- The formula for the nth term of an AP is \(a_n = a + (n-1)d\), where \(a\) is the first term, \(n\) is the number of terms, and \(d\) is the common difference.

- To find the 51st term: \(a_{51} = 4 + (51-1) \times 3 = 4 + 150 = 154\).

- Finding the Median:

- For an odd number of terms, the median is the \(\left(\frac{51 + 1}{2}\right)\)th term.

- This is the 26th term: \(a_{26} = 4 + (26-1) \times 3 = 4 + 75 = 79\).

- Sum of Deviations from the Median:

- In an AP, the sum of deviations of terms from the median is always zero because the AP is symmetric around the median.

Options:

- Option 1: -1

- Option 2: 0

- Option 3: 1

- Option 4: 2

Solution: The sum of deviations from the median is indeed 0.