1. The problem is to find the first quartile (Q1), median (Q2), and third quartile (Q3) of the given data set. 2. First, sort the data in ascending order: $$49, 53, 54, 54, 54, 55, 56, 56, 56, 56, 56, 56, 57, 58, 59, 60, 61, 63, 65, 65, 65, 67, 67, 67, 67, 68, 68, 69, 73, 73, 74, 74, 76, 77, 78, 79, 80, 80, 82, 84, 87, 87, 87, 87, 88, 88, 89, 89, 90, 90$$ 3. There are $n=50$ data points. 4. The median (Q2) is the middle value. Since $n$ is even, median is the average of the 25th and 26th values: $$Q2 = \frac{67 + 68}{2} = 67.5$$ 5. The first quartile (Q1) is the median of the lower half (first 25 values): The 13th value is 57, the 14th is 58, so $$Q1 = \frac{57 + 58}{2} = 57.5$$ 6. The third quartile (Q3) is the median of the upper half (last 25 values): The 38th value is 79, the 39th is 80, so $$Q3 = \frac{79 + 80}{2} = 79.5$$ 7. Summary: - $Q1 = 57.5$ - $Q2 = 67.5$ - $Q3 = 79.5$ These quartiles divide the data into four equal parts, helping understand the distribution.