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.

0 | 3 8
1 | 0 4 5 8
2 | 0 0 0 7 8 8 9
3 | 0 0 0 2 4 5 7 8 9
4 | 2 3 7 8 9
5 | 0
key: 3 | 0 = 30

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

find the mode(s) select the correct choice below and, if necessary, fill in
the answer box to complete your choice.
a. the mode(s) is/are
(use a comma to separate answers as needed.)
b. the mode cannot be calculated because the sample size is too small
c. the mode cannot be calculated because each data entry occurs exactly once
d. the mode cannot be calculated because the data are at the nominal level of measurement

Explanation:

Part 1: Analyzing the Median Representation

The median is the middle value (or average of two middle values) in a sorted dataset, representing the center as it splits data into two equal halves. Option A is correct because the median’s definition is to represent the center. Option B is wrong (median can be a data entry or average, but still represents center). Options C and D are wrong (median isn’t greatest/least entry). Option E is wrong (all datasets with at least one entry have a median).

Step 1: List all data points from the stem - and - leaf plot

• Stem 0: 03, 08 (values: 3, 8)
• Stem 1: 10, 14, 15, 18 (values: 10, 14, 15, 18)
• Stem 2: 20, 20, 20, 27, 28, 28, 29 (values: 20, 20, 20, 27, 28, 28, 29)
• Stem 3: 30, 30, 30, 32, 34, 35, 37, 38, 39 (values: 30, 30, 30, 32, 34, 35, 37, 38, 39)
• Stem 4: 42, 43, 47, 48, 49 (values: 42, 43, 47, 48, 49)
• Stem 5: 50 (value: 50)

Step 2: Count the frequency of each value

• 3: 1; 8: 1; 10: 1; 14: 1; 15: 1; 18: 1; 20: 3; 27: 1; 28: 2; 29: 1; 30: 3; 32: 1; 34: 1; 35: 1; 37: 1; 38: 1; 39: 1; 42: 1; 43: 1; 47: 1; 48: 1; 49: 1; 50: 1

Step 3: Identify the mode(s)

The mode is the value(s) with the highest frequency. Here, 20 and 30 both have a frequency of 3, which is the highest frequency among all values.

Answer:

A. The median represents the center of the data set.

Part 2: Finding the Mode