There are 60 students in a class. The following is the frequency distribution of marks obtained by the students in a test: Marks:, 0, 1, 2, 3, 4, 5 Frequency , `x-2` , `x` , `x^2` , `(x+1)^2` , `2x` , `x+1`. Determine mean and standard deviation of the marks.

Explanation

To solve the problem step by step, we will first determine the value of \( x \) using the given frequency distribution, and then we will calculate the mean and standard deviation of the marks obtained by the students.

### Step 1: Determine the value of \( x \)

We know that the total frequency of students is 60. Therefore, we can set up the equation:

\[
(x - 2) + x + x^2 + (x + 1)^2 + 2x + (x + 1) = 60
...