Question

The durations (minutes) of 26 electric power outages in the community of Sonando Heights over the past five years are shown below.

39 48 22 68 24 15 52 13 49 1 13 43 41 99 31 19 13 52 20 3 17 26 92 24 15 20

Find the mean, median, and mode. (Round your answers to 2 decimal places.)

Descriptive Statistics Data Mean Median Mode

(b) Are the mean and median about the same?

(yes or NO), the mean (Greater than or Less than) is the median.

(c) Is the mode a good measure of center for this data set?

Yes or No

(d) Is the distribution skewed?

Yes, the distribution is skewed left.

Yes, the distribution is skewed right.

No, the distribution is symmetric.

Answer 1

for the given sample

1, 3, 13, 13, 13, 15, 15, 17, 19, 20, 20, 22, 24, 24, 26, 31, 39, 41, 43, 48, 49, 52, 52, 68, 92, 99

The mean is calculated as:

Mean = (1 + 3 + 13 + 13 + 13 + 15 + 15 + 17 + 19 + 20 + 20 + 22 + 24 + 24 + 26 + 31 + 39 + 41 + 43 + 48 + 49 + 52 + 52 + 68 + 92 + 99)/26
= 859/26
Mean = 33.0385

Median is the middle value hence the median is between 13th and 14th value which is (24+24)/2 =24

Mode is the most occuring value of the dataset, hence now since 13, appeared 3 times hence the mode is 13.

b) From the calculation of mean, median and mode it is observed that mean is greater than Median.

c) No mode is not the best measure of the center of the distribution, because the mode is used when the distribution is categorical.

d) Yes, the distribution is skewed right. because the mean is greater than the median and the mode.