The range of a data set is the greatest value minus the least value. In this data set, the least value is $1$ and the greatest value is $8$. So the range is $8-1=7$. Therefore, the correct answer is $7$.

Since the mean of the 4 scores is 81, their total must be $4(81)=324$. The three known scores add to $72+80+84=236$, so $x=324-236=88$. Check the median: the scores in order are 72, 80, 84, 88. The median is the average of the two middle numbers, so $\frac{80+84}{2}=82$, which matches the condition. Therefore, the value of $x$ is 88.

To find the median, first list the 5 values in order from least to greatest: $35,38,40,42,45$. Since there are 5 numbers, the median is the middle value, which is the third number in the ordered list. The third number is $40$, so the median number of customers served is $40$.

To find the median, list the numbers in order: $6,8,8,10,12$. Since there are 5 values, the median is the middle value, which is the third number. The third number is $8$, so the statement that must be true is that the median is $8$.

The range of a data set is the greatest value minus the least value. The longest board is 26 inches and the shortest board is 18 inches, so the range is $26-18=8$. Therefore, the correct answer is 8.