Question

Question 2 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? Question 3

Answer 1

Question 2

a)   We create a frequency table with class width = 20  
   Percentage Distribution = Frequency/Total observations  

Class	Frequency	Percentage Distribution
0-20	15	0.3
21-40	21	0.42
41-60	2	0.04
61-80	3	0.06
81-100	2	0.04
101-120	2	0.04
121-140	3	0.06
141-160	1	0.02
161-180	1	0.02

b)   Histogram

Histogram Frequency Frequency 20 40 60 160 180 80 100 120 140 Days for resolution of the complaint

c)   As can be seen from the percentage, distribution,                       
   72% of the complaints are resolved in 40 days                      
   We can tell the President of the company that                      
   Majority of the complaints are resolved within 40 days of receiving the complaints,                      
   So the customer should expect a complaint to be resolved within 40 days                      
                          
d)   Following table gives the summary statistics and the Excel functions used for calculating the summary statistics          

Description	Formula in Excel	Value
Mean	AVERAGE(data)	43.04
Median	MEDIAN(data)	28.5
First Quartile	QUARTILE.INC(data, 1)	15.25
Third Quartile	QUARTILE.INC(data, 3)	53.5

e)   

Description	Formula in Excel	Value
Range	Max(data)-Min(data)	164
InterQuartile Range	Third Quartile - First Quartile (=53.5-15.25)	38.25
Variance	Var.s(data)	1757.79
Standard Deviation	Stdev.s(data)	41.93

f)   Box Plot

0 20 40 60 80 100 120 140 160

Since bulk observations are on the lower end of the scale  
the data is skewed to the right direction