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 \mid 0 = 30\\)

a. the mode(s) is/are 29,37.
(use a comma to separate answers as needed.)
b. the mode cannot be calculated because the data are at the nominal level of measurement.
c. the mode cannot be calculated because the sample size is too small.
d. the mode cannot be calculated because each data entry occurs exactly once.

does(do) the mode(s) represent a typical entry of the data? choose the correct answer below.
a. the mode(s) does(do) represent a typical entry of the data set.
b. the mode(s) does(do) not represent the center because it(they) is(are) the greatest data entry(ies).
c. the mode(s) does(do) not represent the center because it(they) is(are) the least data entry(ies).
d. the mode(s) does(do) not represent the center because it(they) is(are) not a data entry(ies).
e. the data set does not have a mode.

Explanation:

Reconstruct the dataset from the stem-and-leaf plot

$$
LATEXBLOCK0
$$

Determine the frequency of each value to find the mode

$$
LATEXBLOCK1
$$

$$ \text{Modes} = 29, 37 $$

Evaluate if the modes represent a typical entry of the data set

$$
LATEXBLOCK2
$$

$$ \text{Since } 29 \text{ and } 37 \text{ lie near the center of the distribution, they represent typical entries.} $$

Answer:

Question 1

• A. The mode(s) is/are 29,37 . (Correct answer)
• B. The mode cannot be calculated because the data are at the nominal level of measurement.
• C. The mode cannot be calculated because the sample size is too small.
• D. The mode cannot be calculated because each data entry occurs exactly once.

Question 2

• A. The mode(s) does(do) represent a typical entry of the data set. (Correct answer)
• B. The mode(s) does(do) not represent the center because it(they) is(are) the greatest data entry(ies).
• C. The mode(s) does(do) not represent the center because it(they) is(are) the least data entry(ies).
• D. The mode(s) does(do) not represent the center because it(they) is(are) not a data entry(ies).
• E. The data set does not have a mode.