Question: Determine the average rate of change in median age per year from 1930 to 1960 using the given data: Year 1930 with median age 24.3 and Year 1960 with median age 22.8.
1. **State the problem:** We need to find the average rate of change in the median age of American men at first marriage from the year $1930$ to $1960$.
2. **Formula for average rate of change:**
$$\text{Average rate of change} = \frac{\text{Change in median age}}{\text{Change in years}} = \frac{y_2 - y_1}{x_2 - x_1}$$
where $y_1$ and $y_2$ are median ages at years $x_1$ and $x_2$ respectively.
3. **Identify values:**
- $x_1 = 1930$, $y_1 = 24.3$
- $x_2 = 1960$, $y_2 = 22.8$
4. **Calculate change in median age:**
$$y_2 - y_1 = 22.8 - 24.3 = -1.5$$
5. **Calculate change in years:**
$$x_2 - x_1 = 1960 - 1930 = 30$$
6. **Calculate average rate of change:**
$$\frac{y_2 - y_1}{x_2 - x_1} = \frac{-1.5}{30}$$
7. **Simplify the fraction:**
$$\frac{-1.5}{30} = \frac{\cancel{-1.5}}{\cancel{30}} = -0.05$$
8. **Interpretation:** The median age decreases by $0.05$ years per year on average from 1930 to 1960.
**Final answer:** The average rate of change is $-0.05$ years of age per year, which corresponds to option c.