The problem asks to calculate the mean mark obtained by the members of a class in terms of $a$, $b$, $c$, $x$, $y$, and $z$, where $x$, $y$, $z$ represent the marks and $a$, $b$, $c$ represent the corresponding frequencies.

1. Problem Description

The problem asks to calculate the mean mark obtained by the members of a class in terms of $a$, $b$, $c$, $x$, $y$, and $z$, where $x$, $y$, $z$ represent the marks and $a$, $b$, $c$ represent the corresponding frequencies.

2. Solution Steps

The mean is calculated by dividing the sum of the products of each mark and its frequency by the total number of marks.

The sum of the products of marks and frequencies is $ax + by + cz$.

The total number of marks is $a + b + c$.

The mean mark is:

$$$$

\text{Mean} = \frac{\text{Sum of (mark } \times \text{ frequency)}}{\text{Total number of marks}}

$$$$

$$$$

\text{Mean} = \frac{ax + by + cz}{a + b + c}

$$$$

3. Final Answer

The mean mark is $\frac{ax + by + cz}{a + b + c}$.