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 median is 30.5.
(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.

does the median represent the center of the data? choose the correct answer below.
a. the median represents the center of the data set.
b. the median does not represent the center because it is not a data entry.
c. the median does not represent the center because it is the greatest data entry.
d. the median does not represent the center because it is the least data entry.
e. the data set does not have a median.

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 median is 30.5.
(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.

does the median represent the center of the data? choose the correct answer below.
a. the median represents the center of the data set.
b. the median does not represent the center because it is not a data entry.
c. the median does not represent the center because it is the greatest data entry.
d. the median does not represent the center because it is the least data entry.
e. the data set does not have a median.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Stem-and-Leaf Plot", "Median Calculation", "Measures of Central Tendency Interpretation" ], "new_concepts": [], "current_concepts": [ "Stem-and-Leaf Plot", "Median Calculation", "Measures of Central Tendency Interpretation" ] } ## List the data values from the stem-and-leaf plot $$ \begin{aligned} &\text{Stem 0: } 4, 5 \ &\text{Stem 1: } 13, 14, 17, 19 \ &\text{Stem 2: } 24, 26, 27, 27, 29, 29, 29 \ &\text{Stem 3: } 30, 31, 32, 35, 36, 37, 37, 37, 38 \ &\text{Stem 4: } 41, 42, 45, 46, 48 \ &\text{Stem 5: } 52 \ &N = 2 + 4 + 7 + 9 + 5 + 1 = 28 \end{aligned} $$ ## Calculate the median of the data set $$ \begin{aligned} &\text{Position of median: } \frac{28 + 1}{2} = 14.5 \ &x_{14} = 30,\quad x_{15} = 31 \ &\text{Median} = \frac{30 + 31}{2} = 30.5 \end{aligned} $$ ## Determine if the median represents the center $$ \begin{aligned} &\text{The median (30.5) lies in the middle of the ordered data set.} \ &\text{Therefore, the median represents the center of the data set.} \end{aligned} $$ ## Question 1 A. The median is 30.5.

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. ## Question 2 A. The median represents the center of the data set.

B. The median does not represent the center because it is not a data entry.

C. The median does not represent the center because it is the greatest data entry.

D. The median does not represent the center because it is the least data entry.

E. The data set does not have a median.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Median Calculation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

List the data values from the stem-and-leaf plot

Calculate the median of the data set

Determine if the median represents the center

Answer:

Question 1

Question 2