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 is 30.4.
(round to one decimal place as needed.)
b. the mean cannot be calculated because the data are at the nominal level of measurement.
c. the mean cannot be calculated because the sample size is too small.
d. the mean cannot be calculated because there is an even number of data entries.

does the mean represent the center of the data? choose the correct answer below.
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.

Explanation:

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

$$
LATEXBLOCK0
$$

$$ N = 28 $$

Calculate the mean of the data set

$$
LATEXBLOCK1
$$

$$ \mu = \frac{851}{28} \approx 30.3928 \approx 30.4 $$

Determine if the mean represents the center

$$
LATEXBLOCK2
$$

Answer:

Question 1

• A. The mean is 30.4. (Correct answer)
• B. The mean cannot be calculated because the data are at the nominal level of measurement.
• C. The mean cannot be calculated because the sample size is too small.
• D. The mean cannot be calculated because there is an even number of data entries.

Question 2

• 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.