What is the average of the mean, median and range of the data: $34,41,6,13,27,20,48,$ and $55$?

First, let us arrange the given data in ascending order:
$$6,13,20,27,34,41,48,55$$
Number of terms ($n$) = $8$ 1. Mean:
$$\text{Mean}=\frac{6+13+20+27+34+41+48+55}{8}=\frac{244}{8}=30.5$$
2. Median:Since $n=8$ (even), the median is the average of the $4^{\text{th}}$ and $5^{\text{th}}$ terms:
$$\text{Median}=\frac{27+34}{2}=\frac{61}{2}=30.5$$
3. Range:
$$\text{Range}=\text{Maximum value}-\text{Minimum value}=55-6=49$$
Now, we calculate the average of Mean, Median, and Range:
$$\text{Average}=\frac{\text{Mean}+\text{Median}+\text{Range}}{3}$$
$$\text{Average}=\frac{30.5+30.5+49}{3}=\frac{110}{3}\approx 36.67$$