Questions: The data show the distance (in miles) from an airport of a sample of 22 inbound and outbound airplanes. Use technology to answer parts (a) and (b). a. Find the data set's first, second, and third quartiles. b. Draw a box-and-whisker plot that represents the data set. 3.3 1.9 2.1 3.1 2.7 2.3 2.3 4.1 2.4 5.7 5.9 3.8 5.2 3.9 2.3 4.8 4.8 5.8 3.3 5.1 5.1 2.5 a. Find the three quartiles. Q1= Q2= Q3= (Type integers or decimals. Do not round.) b. Choose the correct box-and-whisker plot below.

Solution Steps

First, we need to organize the data in ascending order: 1.9, 2.1, 2.3, 2.3, 2.5, 2.7, 3.1, 3.3, 3.3, 3.4, 3.8, 4.1, 4.2, 4.3, 4.8, 5.1, 5.2, 5.3, 5.8, 5.9, 6.3, 7.1

The median (Q2) is the middle value of the data set. Since there are 22 data points, the median will be the average of the 11th and 12th values: Q2 = (3.8 + 4.1) / 2 = 3.95

The first quartile (Q1) is the median of the first half of the data set (the first 11 values): Q1 = 3.1

The third quartile (Q3) is the median of the second half of the data set (the last 11 values): Q3 = 5.2

Based on the quartiles calculated:

• Q1 = 3.1
• Q2 = 3.95
• Q3 = 5.2

The correct box-and-whisker plot is the one that matches these quartiles. By examining the options, we find that option B is the correct one.

Final Answer