Question

One of the major measures of the quality of service provided by any organization is the speed with which the organization responds to customer complaints. A large family-held department selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. During a recent year, the company got 50 complaints concerning carpet installation. The following data represent the number of days between the receipt of the complaint and the resolution of the complaint:

54,5,35,137,31,27,152,2,123,81,74,27,11,19,126,110,110,29,61,35,94,31,26,5,12,4,165, 32,29,28,29,26,25,1,14,13,13,10,5,27,4,52,30,22,36,26,20,23,33,68

a. Construct a frequency distribution and a percentage distribution table.

b. Construct a histogram.

c. If you had to tell the president of the company how long a customer should expect to wait to have a complaint resolved, what would you say? Explain.

d. Compute the mean, median, first quartile, and third quartile.

e. Compute the range, interquartile range, variance, standard deviation.

f. Construct a box plot. Are the data skewed? If so, how?

Answer 1

Answer:

Given that,

One of the major measures of the quality of service provided by any organization is the speed with which the organization responds to customer complaints.

A large family-held department selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measure, and 15 installation crews.

During a recent year, the company got 50 complaints concerning carpet installation.

The following data represent the number of days between the receipt of the complaint and the resolution of the complaint:

54,5,35,137,31,27,152,2,123,81,74,27,11,19,126,110,110,29,61,35,94,31,26,5,12,4,165, 32,29,28,29,26,25,1,14,13,13,10,5,27,4,52,30,22,36,26,20,23,33,68

(a).

Frequency distribution and percentage distribution:

Here we can use class width =30 for frequency distribution.

Percentage distribution=Frequency/Number of observations

Number of observations=50

Class	Frequency	Percentage
0-29	28	56%
30-59	10	20%
60-89	4	8%
90-119	3	6%
120-149	3	6%
150-179	2	4%
Total	50	100%

(b).

Histogram:

(c).

We can observe percentage distribution 56% of the complaints are resolved in 30 days.

Majority of the complaints are resolved within 30 days of receiving complaints.

Hence we can tell the president of the company that customers should expect a complaint to be resolved within 30 days.

(d).

Mean, Median, First quartile and Third quartile:

Mean:

Mean= (Sum of terms)/(Number of terms)

=(54+5+.........+33+68)/50

=2152/50

=43.04

Median:

First arrange the data in ascending order then we find the median i.e, average pair of middle numbers. So, we have

Median=(28+29)/2

=28.5

First quartile(Q₁):

Arrange the first half data into ascending order.

Then, we have

1,2,4,4,5,5,5,10,11,12,13,14,19,20,22,23,25,26,26,26,27,27,27,28

Here Median=14

First qyartile (Q₁)=14

Third qyartile (Q₃):

Arrange the second half data in ascending order

Then,

29,29,29,30,31,31,32,33,35,35,36,52,54,61,68,74,81,94,110,110,123,126,137,152,165

Here, median=54

Third quartile(Q₃)=54

(e).

Range:

From the given lowest value=1 and highest value=165

So, range 165-1=164

Range=164

Inter quartile range:

from the above First quartile=14 and,

Third quartile=54

1QR=Q₃-Q₁

=54-14

=40

Inter quartile range=40

Variance:

where , N=50

=86131.92/49

=1757.7943

Variance=1757.7943

Standard deviation:

=41.9216

Standard deviation=41.9216

(f).

Box Plot:

Here Q₁=14 and Q₂=28.5, Q₃=54

Since maximum observations are on the lower end of the scale. So, the data is skewed to the right.