Answer
4
Work Step by Step
Three data points aren't possible since the mode would be listed twice and the mode is not the same as the median.
Four data points made the data possible. The mode would be listed at least twice. $(6.6, 6.6)$
The median (for data sets with an even number of data points) is the average of the two middle data points. We know one data point (6.6) and the median (6.8), so we can determine the third data point to be 7.0. $(.5*(6.6+7) = 6.8)$
We know the mean is 7.8, so we also know the sum of the data points is 31.2. We know three of the four data points (6.6, 6.6, 7), so we can find the final data point:
$(6.6+6.6+7+x)/4=7.8$
$6.6+6.6+7+x = 31.2$
$20.2 + x = 31.2$
$x = 11$
