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

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.

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

a. the median duration is 58.5 minutes.
(round to one decimal place as needed.)
b. there is no median score.

does the median represent the center of the data?

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

Explanation:

Sort the data set

$$ 12, 27, 37, 43, 53, 64, 84, 84, 127, 127 $$

Calculate the median

$$
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$$

Determine if the median represents the center

$$ \text{The median represents the center of the data set because it lies in the middle of the sorted values.} $$

Answer:

Question 1

• (A) The median duration is 58.5 minutes. (Correct answer)
• (B) There is no median score.

Question 2

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