Final answer:
To create a box-and-whisker plot, arrange the data in ascending order and find the minimum value, first quartile, median, third quartile, and maximum value. Then, construct the plot using these values.
Step-by-step explanation:
To create a box-and-whisker plot, you need to first find the minimum value, first quartile, median, third quartile, and maximum value from the given data set. Let's go step-by-step:
Step 1: Arrange the data in ascending order: 2, 5, 7, 8, 9, 9, 10, 11, 14, 15, 18, 22, 25, 27, 27.
Step 2: Find the minimum value, which is 2.
Step 3: Find the first quartile (Q1). Since there are 15 data points, Q1 will be the median of the lower half of the data set. The lower half is: 2, 5, 7, 8, 9, 9. The median of this set is (7 + 8) / 2 = 7.5.
Step 4: Find the median (Q2). Since there are 15 data points, the median will be the middle value. The middle value is 10.
Step 5: Find the third quartile (Q3). Since there are 15 data points, Q3 will be the median of the upper half of the data set. The upper half is: 14, 15, 18, 22, 25, 27. The median of this set is (18 + 22) / 2 = 20.
Step 6: Find the maximum value, which is 27.
Step 7: Now we can construct the box-and-whisker plot using the minimum value, Q1, Q2, Q3, and the maximum value.