The following refer to the following data set: \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline 93 & 23 & 60 & 67 & 84 & 87 & 60 & 48 & 37 & 54 \\ \hline \end{tabular} What is the mean $(\overline{\bar{x}})$ of this data set? \[ \text { mean }= \] (Please show your answer to one decimal place.) What is the median of this data set? \[ \text { median }= \] What is the mode of this data set? \[ \text { mode }= \]

Step 1 ：Given the data set: [93, 23, 60, 67, 84, 87, 60, 48, 37, 54]

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

Step 3 ：Calculating the mean of the given data set, we get \(\frac{93 + 23 + 60 + 67 + 84 + 87 + 60 + 48 + 37 + 54}{10} = 61.3\)

Step 4 ：The median of a data set is the middle number when the numbers are listed in numerical order. If there is an even number of observations, the median is the average of the two middle numbers.

Step 5 ：Arranging the given data set in numerical order, we get: [23, 37, 48, 54, 60, 60, 67, 84, 87, 93]

Step 6 ：Since there are 10 numbers in the data set, an even number, the median is the average of the 5th and 6th numbers. So, the median is \(\frac{60 + 60}{2} = 60.0\)

Step 7 ：The mode of a data set is the number that appears most frequently. In the given data set, the number 60 appears twice, which is more than any other number.

Step 8 ：So, the mode of the data set is 60.

Step 9 ：Final Answer: The mean of the data set is \(\boxed{61.3}\), the median is \(\boxed{60.0}\), and the mode is \(\boxed{60}\)