The problem is to create a box plot for the dataset {9, 15, 19, 5, 20, 15}. We need to order the data, find the median, the lower quartile median, and the upper quartile median. Then draw a box plot.

1. Problem Description

The problem is to create a box plot for the dataset {9, 15, 19, 5, 20, 15}. We need to order the data, find the median, the lower quartile median, and the upper quartile median. Then draw a box plot.

2. Solution Steps

First, we order the numbers from least to greatest:

5, 9, 15, 15, 19, 20

Next, we find the median of all the data. Since there are 6 numbers, the median is the average of the two middle numbers, which are 15 and

1

5. Median $= \frac{15 + 15}{2} = \frac{30}{2} = 15$

Now, we find the lower quartile median. This is the median of the numbers less than the median of the whole data set. The numbers are 5, 9,

1

5. The median of these numbers is

9. Lower Quartile Median $= 9$

Next, we find the upper quartile median. This is the median of the numbers greater than the median of the whole data set. The numbers are 15, 19,

2

0. The median of these numbers is

1

9. Upper Quartile Median $= 19$

The least number is

5. The greatest number is

2

0.

Now we can create the box plot. We need to draw a number line that includes all the numbers from 5 to

2

0. Plot the least number (5), the greatest number (20), the median (15), the lower quartile median (9), and the upper quartile median (19). Draw a box from the lower quartile median (9) to the upper quartile median (19). Draw a vertical line through the median (15). Connect the least number (5) to the box (whisker) and the greatest number (20) to the box (whisker).

3. Final Answer

The box plot would have the following key values:

Minimum value: 5

Lower Quartile (Q1): 9

Median (Q2): 15

Upper Quartile (Q3): 19

Maximum value: 20

A box is drawn from 9 to

1

9. A line is drawn within the box at

1

5. The whiskers extend from 5 to 9 and from 19 to

2

0.