Questions: To the right is a stem-and-leaf display representing the amount of gasoline purchased, in gallons (with leaves in tenths of gallons), for a sample of 25 cars that use a particular service station on the New Jersey Turnpike. Complete parts (a) through (d). 9 10 13469 11 12344589 12 014468 13 278 a. Place the data into an ordered array. Choose the correct answer below. A. 9.59 .99 .910 .110 .310 .410 .610 .911 .111 .211 .311 .411 .411 .511 .811 .912 .012 .112 .412 .412 .612 .813 .213 .713 .8 B. 9.510 .111 .112 .013 .29 .910 .311 .212 .113 .79 .910 .411 .312 .410 .611 .412 .410 .911 .412 .611 .512 .811 .811 .913 .8 C. 13.813 .713 .212 .812 .612 .412 .412 .112 .011 .911 .811 .511 .411 .411 .311 .211 .110 .910 .610 .410 .310 .19 .99 .99 .5 b. Which of these two displays seems to provide more information? stem-and-leaf display ordered array c. What amount of gasoline (in gallons) is most likely to be purchased? gallons (Type a whole number.)

Solution Steps

The stem-and-leaf display is given as: \[ \begin{tabular}{rl} 9 & \multicolumn{3}{|l}{} \\ 10 & 13469 \\ 11 & 12344589 \\ 12 & 014468 \\ 13 & 278 \end{tabular} \] To convert this into an ordered array, we interpret each stem and its corresponding leaves. For example:

• Stem 9 has no leaves, so it is ignored.
• Stem 10 with leaves 1, 3, 4, 6, 9 corresponds to 10.1, 10.3, 10.4, 10.6, 10.9.
• Stem 11 with leaves 1, 2, 3, 4, 4, 5, 8, 9 corresponds to 11.1, 11.2, 11.3, 11.4, 11.4, 11.5, 11.8, 11.9.
• Stem 12 with leaves 0, 1, 4, 4, 6, 8 corresponds to 12.0, 12.1, 12.4, 12.4, 12.6, 12.8.
• Stem 13 with leaves 2, 7, 8 corresponds to 13.2, 13.7, 13.8.

The ordered array is: \[ 9.5, 10.1, 10.3, 10.4, 10.6, 10.9, 11.1, 11.2, 11.3, 11.4, 11.4, 11.5, 11.8, 11.9, 12.0, 12.1, 12.4, 12.4, 12.6, 12.8, 13.2, 13.7, 13.8 \] This matches option A.

The stem-and-leaf display provides a visual representation of the data distribution, showing the frequency of values within each stem. It also retains the original data values, making it easier to identify patterns, clusters, or outliers.

The ordered array lists all the data points in ascending order, which is useful for identifying the minimum, maximum, and range of the data. However, it does not provide a visual representation of the distribution.

The stem-and-leaf display provides more information because it combines the benefits of both a visual representation and the retention of raw data.

The most likely amount of gasoline purchased corresponds to the mode of the data, which is the value that appears most frequently. From the ordered array: \[ 11.4 \text{ appears twice}, \text{ while all other values appear once.} \] Thus, the most likely amount of gasoline purchased is: \[ 11.4 \text{ gallons.} \]

Final Answer