To calculate the sample mean height, you need to add up all the heights and then divide by the number of heights.
The heights are: {64, 67, 65, 71, 73, 69}.
First, sum all the heights:
\[ 64 + 67 + 65 + 71 + 73 + 69 = 409 \]
Next, divide the total by the number of heights (which is 6):
\[ \text{Mean} = \frac{409}{6} \approx 68.1667 \]
Rounding to the nearest inch gives us:
\[ \text{Mean} \approx 68 \]
So the answer is 68.