Step 1 :First, we need to sort the data set in ascending order. The sorted data set is \[1, 1, 7, 9, 10, 11, 15, 27, 34\].
Step 2 :To find the mean, we add up all the numbers in the data set and divide by the number of items in the data set. The mean is \(\frac{1+1+7+9+10+11+15+27+34}{9} \approx 12.8\).
Step 3 :The median is the middle number in a sorted data set. Since our data set has 9 items, the median is the 5th item, which is 10.
Step 4 :The mode is the number that appears most frequently in the data set. In our data set, the number 1 appears twice, more than any other number, so the mode is 1.
Step 5 :The midrange is the average of the smallest and largest numbers in the data set. The midrange is \(\frac{1+34}{2} = 17.5\).
Step 6 :Final Answer: The mean of the data set is \(\boxed{12.8}\), the median is \(\boxed{10}\), the mode is \(\boxed{1}\), and the midrange is \(\boxed{17.5}\).