1. The problem asks to find the mean height of two black bars and adjust a light bar to that mean height. 2. The mean (average) of two numbers $a$ and $b$ is given by the formula: $$\text{Mean} = \frac{a + b}{2}$$ 3. Important rule: The mean is the sum of the values divided by the number of values. 4. Let the height of the taller black bar be $h$ and the shorter black bar be approximately $\frac{h}{2}$. 5. Substitute these values into the mean formula: $$\text{Mean} = \frac{h + \frac{h}{2}}{2}$$ 6. Simplify the numerator: $$\frac{h + \frac{h}{2}}{2} = \frac{\frac{2h}{2} + \frac{h}{2}}{2} = \frac{\frac{3h}{2}}{2}$$ 7. Simplify the fraction by dividing by 2: $$\frac{\frac{3h}{2}}{2} = \frac{3h}{2} \times \frac{1}{2} = \frac{3h}{4}$$ 8. So, the mean height is: $$\boxed{\frac{3h}{4}}$$ 9. This means the light bar should be adjusted to $\frac{3}{4}$ of the taller black bar's height to represent the mean height of the two black bars.