First fi nd Q1 , Q2 and Q3 and then draw box plots for the given datasets. Remember to fi nd outliersand mark them on your box plot if they exist.a 11, 15, 18, 17, 1, 2, 8, 12, 19, 15

To find Q1, Q2, and Q3 and draw box plots for the given datasets, follow these steps:

1. Arrange the data in ascending order: 1, 2, 8, 11, 12, 15, 15, 17, 18, 19.

2. Find the median (Q2). Since we have an even number of data points, the median is the average of the two middle numbers. In this case, (12 + 15) / 2 = 13.5.

3. Q1 is the median of the first half of the data. Since we have an even number of data points, we include the median in both halves. So, Q1 is the median of 1, 2, 8, 11, 12. This is (8 + 11) / 2 = 9.5.

4. Q3 is the median of the second half of the data. So, Q3 is the median of 12, 15, 15, 17, 18, 19. This is (15 + 17) / 2 = 16.

5. To find outliers, we first need to find the interquartile range (IQR), which is Q3 - Q1 = 16 - 9.5 = 6.5. Any data point that is less than Q1 - 1.5IQR or greater than Q3 + 1.5IQR is considered an outlier. In this case, Q1 - 1.5IQR = 9.5 - 1.56.5 = -0.75 and Q3 + 1.5IQR = 16 + 1.56.5 = 26.25. So, any data point less than -0.75 or greater than 26.25 is an outlier. In this dataset, there are no outliers.

6. Now, you can draw your box plot. The box is formed by Q1 and Q3, with a line inside the box for Q2. The "whiskers" extend from the box to the smallest and largest data points that are not outliers. In this case, the whiskers would extend to 1 and 19. Since there are no outliers, there are no points outside the whiskers.