Question

create a box plot using the following set of data. 13, 16, 19, 15, 20, 19, 9

Explanation:

Step1: Order the data

First, we need to order the data set from smallest to largest. The data set is \( 13, 16, 19, 15, 20, 19, 9 \). When ordered, it becomes \( 9, 13, 15, 16, 19, 19, 20 \).

Step2: Find the median (Q2)

The median is the middle value of the ordered data set. Since there are 7 data points (an odd number), the median is the 4th value. So, the median \( Q2 = 16 \).

Step3: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data. The lower half of the data (excluding the median) is \( 9, 13, 15 \). The median of this subset is the 2nd value, so \( Q1 = 13 \).

Step4: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data. The upper half of the data (excluding the median) is \( 19, 19, 20 \). The median of this subset is the 2nd value, so \( Q3 = 19 \).

Step5: Identify the minimum and maximum

The minimum value in the data set is \( 9 \) and the maximum value is \( 20 \).

Step6: Construct the box plot

• Draw a number line that includes the range from the minimum (9) to the maximum (20).
• Draw a box from \( Q1 = 13 \) to \( Q3 = 19 \). Inside the box, draw a vertical line at the median \( Q2 = 16 \).
• Draw whiskers from the box to the minimum (9) and to the maximum (20).

Answer:

The box plot is constructed with minimum = 9, \( Q1 = 13 \), median = 16, \( Q3 = 19 \), and maximum = 20. The box spans from 13 to 19, with a line at 16, and whiskers extending to 9 and 20.