Listed below are the amounts of time (in months) that the employees of a restaurant have been working at the restaurant. Find the mean for the given sample data. Round your answer to one more decimal place than the original data values.
$\begin{array}{llllllllllllll}1 & 5 & 6 & 8 & 11 & 14 & 17 & 46 & 61 & 90 & 99 & 126 & 143 & 167\end{array}$
A. 31.5 months
B. 61.1 months
c. 56.7 months
D. 52.9 months

Step 1 ：Given the data set of the amounts of time (in months) that the employees of a restaurant have been working at the restaurant: \[\{1, 5, 6, 8, 11, 14, 17, 46, 61, 90, 99, 126, 143, 167\}\]

Step 2 ：The mean of a set of numbers is calculated by adding all numbers in the set and then dividing by the count of numbers in the set.

Step 3 ：First, add all the months that the employees have been working at the restaurant: \[1 + 5 + 6 + 8 + 11 + 14 + 17 + 46 + 61 + 90 + 99 + 126 + 143 + 167 = 794\]

Step 4 ：Then, divide the total by the number of employees, which is 14: \[\frac{794}{14} = 56.714285714285715\]

Step 5 ：Round the result to one more decimal place than the original data values, which gives approximately 56.7.

Step 6 ：Final Answer: The mean for the given sample data is approximately \(\boxed{56.7}\) months.