Question

the weights, in pounds, of packages on a delivery truck are shown in the stem-and-leaf plot. find the mean, the median, and the mode of the data, if possible. if any measure cannot be found or does not represent the center of the data, explain why.

\

$$\begin{array}{r|l} 0 & 4 \\; 5 \\\\ 1 & 3 \\; 4 \\; 7 \\; 9 \\\\ 2 & 4 \\; 6 \\; 7 \\; 7 \\; 9 \\; 9 \\; 9 \\\\ 3 & 0 \\; 1 \\; 2 \\; 5 \\; 6 \\; 7 \\; 7 \\; 7 \\; 8 \\\\ 4 & 1 \\; 2 \\; 5 \\; 6 \\; 8 \\\\ 5 & 2 \\end{array}$$

key: 3 | 0 = 30

a. the mean represents the center of the data set.
b. the mean does not represent the center because it is not a data entry.
c. the mean does not represent the center because it is the greatest data entry.
d. the mean does not represent the center because it is the least data entry.
e. the data set does not have a mean.

find the median. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the median is . (round to one decimal place as needed.)
b. the median cannot be calculated because there is an even number of data entries.
c. the median cannot be calculated because the data are at the nominal level of measurement.
d. the median cannot be calculated because the sample size is too small.

Explanation:

Reconstruct the data set from the stem-and-leaf plot

$$
LATEXBLOCK0
$$

Calculate the mean and evaluate its representation

$$
LATEXBLOCK1
$$

The distribution is relatively symmetric without extreme outliers, so the mean represents the center of the data set.

Calculate the median

$$
LATEXBLOCK2
$$

Answer:

Question 1

• A. The mean represents the center of the data set. (Correct answer)
• B. The mean does not represent the center because it is not a data entry.
• C. The mean does not represent the center because it is the greatest data entry.
• D. The mean does not represent the center because it is the least data entry.
• E. The data set does not have a mean.

Question 2

• A. The median is 29.5 (Correct answer)
• B. The median cannot be calculated because there is an even number of data entries.
• C. The median cannot be calculated because the data are at the nominal level of measurement.
• D. The median cannot be calculated because the sample size is too small.