Question

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

32 98 47 30 26 22 68 12 27 50 9 35 58 2 11 25 50 24 4 86 16 29 49 16 38 16

(a) Find the mean, median, and mode

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

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

(d) Is the distribution skewed?

Answer 1

Ansa:

using R-software

> x=scan("clipboard");x
Read 26 items
[1] 32 98 47 30 26 22 68 12 27 50 9 35 58 2 11 25 50
[18] 24 4 86 16 29 49 16 38 16
> mean(x)
[1] 33.84615
> median(x)
[1] 28

#

Also manually

Mean=sum(x)/n=880/26=33.84615

#Median

Arrange the data in increasing order

2
4
9
11
12
16
16
16
22
24
25
26
27
29
30
32
35
38
47
49
50
50
58
68
86
98

#Meadian= ((n/2)+(n/2+1))Th observation/2

=13thobservation +14thobservatioin)/2

=(27+29)/2

=28

#Median=28

Mode=The number which appears most often in a set of numbers.

Mode=16

(b) Are the mean and median about the same?
  
Ansb. no the mean is greater than the median

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

Ans: No

(d) Is the distribution skewed?

Ans: yes,the distribution is skewed left