Step 1 :First, arrange the data in ascending order: \(75, 79, 81, 82, 86, 87, 89, 90, 90, 90, 91, 91, 95, 98, 99, 101, 109, 114, 118\)
Step 2 :To find Q2, find the median of the entire data set. Since there are 19 data points, the median will be the 10th value. So, \(Q2 = 90\)
Step 3 :To find Q1, find the median of the lower half of the data. The lower half of the data is: \(75, 79, 81, 82, 86, 87, 89, 90, 90\). Since there are 9 data points, the median will be the 5th value. So, \(Q1 = 86\)
Step 4 :To find Q3, find the median of the upper half of the data. The upper half of the data is: \(90, 91, 91, 95, 98, 99, 101, 109, 114, 118\). Since there are 10 data points, the median will be the average of the 5th and 6th values. So, \(Q3 = \frac{98 + 99}{2} = 98.5\)
Step 5 :So, the solutions are: \(\boxed{Q2 = 90}\), \(\boxed{Q1 = 86}\), \(\boxed{Q3 = 98.5}\)