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 29.5. (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

$$
LATEXBLOCK0
$$

$$ N = 28 $$

Evaluate the mean and its representation of the center

$$
LATEXBLOCK1
$$

$$ \mu = \frac{816}{28} \approx 29.14 $$

The mean is a typical value near the center of this symmetric/slightly skewed distribution without extreme outliers that would distort it. Thus, the mean represents the center of the data set.

Calculate the median

Since \(N = 28\) is even, the median is the average of the \(14^{\text{th}}\) and \(15^{\text{th}}\) values:

$$
LATEXBLOCK2
$$

The image shows a selected option "A. The median is 29.5" which is incorrect based on the actual data values. The correct median is \(30.5\).

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 30.5. (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.