Step 1 :The given data set is \(2, 10, 3, 2, 8, 12\).
Step 2 :The mean is calculated by summing all the numbers in the data set and then dividing by the number of items in the set.
Step 3 :The median is the middle number in a sorted, ascending or descending, list of numbers. If the list contains an even number of observations, the median is the average of the two middle numbers.
Step 4 :The mode is the number that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.
Step 5 :The mean of the data set is \(6.17\) (rounded to two decimal places), the median is \(5.5\), and the mode is \(2\).
Step 6 :Final Answer: The mean of the data set is \(\boxed{6.17}\), the median is \(\boxed{5.5}\), and the mode is \(\boxed{2}\).