Given the data set: 3, 4, 5, 7, 8, 9, 10, 11, 6, 13, 15, 21, 3. Calculate the average, the mode, and the probability of choosing a value less than 10 as a percentage.

The average of the data set is $\boxed{\text{8.85}}$.

In the sorted data set ($3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21$), the number 3 appears twice, while all other numbers appear only once.
The modal value is $\boxed{3}$.

The values less than 10 are: $3, 3, 4, 5, 6, 7, 8, 9$. There are 8 such values.

The probability of choosing a value less than 10 is $\boxed{61.54\%}$.

$3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 21$.
The number of data points is $n = 13$.

The $7^{\text{th}}$ value in the sorted data set is 8.
The middle value of the data set is $\boxed{8}$.

Highest value = 21
Lowest value = 3

The gap between the highest and lowest value is $\boxed{18}$.