The mean marks of the folloring distribution is

Marks Obtained	No. of Students
81	15
35	4
73	3
56	16

The correct option is 65.

Step-by-step Explanation:

To find the mean marks of a discrete frequency distribution, we use the direct method formula for mean ($\overline{x}$):

$\overline{x}=\frac{\sum f_i{x}_i}{\sum f_i}$

Where:
- $x_i$ represents the marks obtained.
- $f_i$ represents the corresponding number of students (frequency).

Step 1: Calculate the product of marks ($x_i$) and frequency ($f_i$) for each observation.

1. For marks = 81, students = 15:
$f_1{x}_1=81\times 15=1215$

2. For marks = 35, students = 4:
$f_2{x}_2=35\times 4=140$

3. For marks = 73, students = 3:
$f_3{x}_3=73\times 3=219$

4. For marks = 56, students = 16:
$f_4{x}_4=56\times 16=896$

Step 2: Find the sum of all frequencies ($\sum f_i$).

$\sum f_i=15+4+3+16=38$

Step 3: Find the total sum of products ($\sum f_i{x}_i$).

$\sum f_i{x}_i=1215+140+219+896=2470$

Step 4: Compute the mean.

$\overline{x}=\frac{2470}{38}=65$

Thus, the mean marks of the given distribution is 65.