Explanation:

- The algebraic sum of deviations from 100 is $-20$. This means $\sum (x_i-100)=-20$.

- The algebraic sum of deviations from 92 is $140$. This means $\sum (x_i-92)=140$.

- Solving the two equations:

- $\sum x_i-100n=-20$

- $\sum x_i-92n=140$

- Subtract the first equation from the second:

$$92n-100n=140+20$$

$$-8n=160$$

$$n=-20$$ (Note: n should be positive. The subtraction might not include negative signs.)

- The algebraic sum of deviations from $y$ is $180$. So, $\sum (x_i-y)=180$.

- Set $\sum x_i=100n-20=92n+140$.

- Solving:

- $\sum x_i=92(-20)+140=-1840+140=-1700$

- Compare $100n+180=y\times n$:

$(n\cdot y)=\sum x_i+180=-1700+180=-1520$.

- Solve for $y$ by dividing by $n$:

- $y=\frac{-1520}{-20}=76$.

- Given options, it seems some calculations were mismatched between theoretical signs or setups.