Question

find the mean, median, and mode of the data, if possible. if any of these measures cannot be found or a measure does not represent the center of the data, explain why.

the durations (in minutes) of power failures at a residence in the last 4 years are listed below.

27 127 64 84 37 53 84 127 12 43

what is the mean duration? select the correct choice below and fill in any answer box to complete your choice.

a. the mean duration is 65.8 minutes.
(round to one decimal place as needed.)
b. there is no mean score.

does the mean represent the center of the data?

a. the mean represents the center.
b. the mean does not represent the center because it is not a data value.
c. the mean does not represent the center because it is the smallest data value.
d. the mean does not represent the center because it is the largest data value.

Explanation:

Calculate the mean of the data

$$
LATEXBLOCK0
$$

Determine if the mean represents the center

$$
LATEXBLOCK1
$$

The mean value of \(65.8\) lies near the middle of the sorted dataset (between \(64\) and \(84\)) and is not skewed by extreme outliers, thus representing the center of the data.

Answer:

Question 1

• (A) The mean duration is 65.8 minutes. (Correct answer)
• (B) There is no mean score.

Question 2

• (A) The mean represents the center. (Correct answer)
• (B) The mean does not represent the center because it is not a data value.
• (C) The mean does not represent the center because it is the smallest data value.
• (D) The mean does not represent the center because it is the largest data value.