1. The problem asks about the possible values of the average (mean) height of 5 people with heights $h_1 < h_2 < h_3 < h_4 < h_5$. 2. The average height is calculated by the formula: $$\text{Average} = \frac{h_1 + h_2 + h_3 + h_4 + h_5}{5}$$ 3. Since $h_1, h_2, h_3, h_4, h_5$ are in increasing order, the average must lie between the smallest and largest values, i.e., between $h_1$ and $h_5$. 4. The average does not have to be equal to any of the individual heights; it can be any value between $h_1$ and $h_5$ depending on the values of the heights. 5. Therefore, the correct statement is: C The average height can take any value between $h_1$ and $h_5$. Final answer: C