You have been given the following data set: {5, 7, 9, 10, 12, 15, 20}, find the five-number summary.
Solution
Step 1 ：Step 1: Arrange the data in ascending order, which is already done in this case: \(5, 7, 9, 10, 12, 15, 20\).
Step 2 ：Step 2: Identify the minimum value: \(\min = 5\).
Step 3 ：Step 3: Identify the first quartile (Q1). Since there are 7 numbers in our data set, the first quartile is the median of the first half (excluding the median if the number of data points is odd). In this case, Q1 is the median of \(5, 7, 9\), which is \(7\).
Step 4 ：Step 4: Identify the median (Q2). It's the middle number of the data set. In this case, the median is \(10\).
Step 5 ：Step 5: Identify the third quartile (Q3). This is the median of the second half of the data (excluding the median if the number of data points is odd). In this case, Q3 is the median of \(12, 15, 20\), which is \(15\).
Step 6 ：Step 6: Identify the maximum value: \(\max = 20\).
