Question

Call International oversees the quality of 200 call centers throughout the world. They want to determine how the centers compare among four variables for the most recent year:

Shift A Average Call Time (in minutes)
Shift B Average Call Time (in minutes)
Average Customer Satisfaction Level (on a 4-point scale: 1=poor, 2=average, 2=good, 3=excellent)
Average Number of Employees

Data collected for the sample of 200 Call Centers is contained in the file named Call Centers linked at the bottom of the page. Use all 200 data points.

Managerial Report

Prepare a report (see Module folder) using the numerical methods of descriptive statistics presented in this module to learn how the variables contribute to the success of a call center. Be sure to include the following three items in your report.

1. Find descriptive sample statistics (mean, median, range, the two quartiles Q1 and Q3, minimum, maximum, sample standard deviation, and coefficient of variation) for each of the four variables, along with an explanation of what the descriptive statistics tell us about the call centers.
2. Use the z-score to determine which call centers, if any, should be considered outliers in each of the four variables. If there are any outliers in any category, please list them and state for which category they are an outlier.
3. Compute the sample correlation coefficient, showing the relationship between Satisfaction Level and each of the other three variables (Shift A Average Call time, Shift B Average Call Time, Average Number of Employees). Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.

1. Include a title page, introduction, body, conclusion, and a reference page.
2. The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.
3. The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
4. The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
5. Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.

Answer 1

SOLUTION

DESCRIPTIVE STATISTICS:-

Statistics AVG SATISFA | AVG NO OF SHIFTA_AVG SHIFTB_AVG CTION LEVE EMPLOYEE CALL_TIME 200 CALL_TIME 200 Valid Missing 200 200 Mean Median Std. Deviation Range Minimum Maximum Percentiles 25 37.0900 31.5000 28.26013 125.00 1.00 126.00 13.0000 31.5000 55.7500 39.0400 40.0000 21.08891 74.00 1.00 75.00 21.2500 40.0000 57.0000 2.5750 2.0000 1.10929 3.00 1.00 4.00 2.0000 2.0000 4.0000 60.5650 60.0000 22.09950 85.00 15.00 100.00 42.0000 60.0000 77.0000 50 75

First of all there are no missing values. We can study from the above statistics that Standard deviation for all of the variables is quite high which means there is great variation in values of all the variables. Also Range value is high which means greater spread for the data.

So we can infer from the descriptive statistics is that Call centers have great variation in terms average call times for both shifts , average satisfaction level and average number of employees.

Now, we calculate Z scores for each variable by simply subtracting the mean and dividing the difference by standard deviation for each variable. Z score = (x - mean(x)/sd(x))

Now if absolute value of any Z score is greater than 3 ( 3 sigma limits) we can say that it is an OUTLIER.

					Z SCORES
Call Center	Shift A Average Call Time	Shift B Average Call Time	Average Satisfaction Level	Average Number of Employees	Shift A Average Call Time	Shift B Average Call Time	Average Satisfaction Level	Average Number of Employees
1	14	29	2	100	-0.81741	-0.47608	-0.518018	1.78438914
2	1	1	1	90	-1.27742	-1.80378	-1.4189189	1.33190045
3	53	60	4	80	0.562633	0.993883	1.28378378	0.87941176
4	10	25	2	54	-0.95895	-0.66575	-0.518018	-0.2970588
5	85	71	4	69	1.694975	1.515482	1.28378378	0.38167421
6	18	33	2	54	-0.67587	-0.28641	-0.518018	-0.2970588
7	24	40	2	42	-0.46355	0.045521	-0.518018	-0.8400452
8	58	65	4	67	0.739561	1.230973	1.28378378	0.29117647
9	33	46	3	30	-0.14508	0.33003	0.38288288	-1.3830317
10	9	19	1	48	-0.99434	-0.95026	-1.4189189	-0.568552
11	10	23	2	29	-0.95895	-0.76059	-0.518018	-1.4282805
12	6	13	1	26	-1.1005	-1.23477	-1.4189189	-1.5640271
13	31	44	3	27	-0.21585	0.235194	0.38288288	-1.5187783
14	11	28	2	100	-0.92357	-0.5235	-0.518018	1.78438914
15	3	7	1	47	-1.20665	-1.51928	-1.4189189	-0.6138009
16	81	70	4	37	1.553432	1.468064	1.28378378	-1.0662896
17	56	63	4	95	0.66879	1.136137	1.28378378	1.5581448
18	63	67	4	84	0.91649	1.32581	1.28378378	1.06040724
19	8	16	1	53	-1.02972	-1.09251	-1.4189189	-0.3423077
20	55	61	4	77	0.633404	1.041301	1.28378378	0.74366516
21	38	48	3	49	0.031847	0.424866	0.38288288	-0.5233032
22	10	26	2	66	-0.95895	-0.61833	-0.518018	0.2459276
23	3	8	1	49	-1.20665	-1.47186	-1.4189189	-0.5233032
24	7	15	1	94	-1.06511	-1.13993	-1.4189189	1.51289593
25	4	11	1	55	-1.17127	-1.3296	-1.4189189	-0.25181
26	19	34	2	40	-0.64048	-0.23899	-0.518018	-0.930543
27	74	69	4	74	1.305732	1.420646	1.28378378	0.60791855
28	49	57	3	73	0.42109	0.851629	0.38288288	0.56266968
29	22	37	2	44	-0.53432	-0.09673	-0.518018	-0.7495475
30	49	57	3	46	0.42109	0.851629	0.38288288	-0.6590498
31	10	22	2	39	-0.95895	-0.808	-0.518018	-0.9757919
32	7	16	1	69	-1.06511	-1.09251	-1.4189189	0.38167421
33	39	49	3	84	0.067233	0.472284	0.38288288	1.06040724
34	8	17	1	90	-1.02972	-1.04509	-1.4189189	1.33190045
35	9	19	2	96	-0.99434	-0.95026	-0.518018	1.60339367
36	39	49	3	68	0.067233	0.472284	0.38288288	0.33642534
37	29	43	3	93	-0.28662	0.187776	0.38288288	1.46764706
38	116	75	4	66	2.791932	1.705154	1.28378378	0.2459276
39	17	32	2	96	-0.71125	-0.33382	-0.518018	1.60339367
40	11	28	2	96	-0.92357	-0.5235	-0.518018	1.60339367
41	10	23	2	59	-0.95895	-0.76059	-0.518018	-0.0708145
42	19	34	2	67	-0.64048	-0.23899	-0.518018	0.29117647
43	25	40	2	79	-0.42817	0.045521	-0.518018	0.8341629
44	2	4	1	98	-1.24204	-1.66153	-1.4189189	1.6938914
45	4	11	1	69	-1.17127	-1.3296	-1.4189189	0.38167421
46	56	64	4	74	0.66879	1.183555	1.28378378	0.60791855
47	61	66	4	67	0.845718	1.278392	1.28378378	0.29117647
48	66	67	4	100	1.022647	1.32581	1.28378378	1.78438914
49	18	33	2	38	-0.67587	-0.28641	-0.518018	-1.0210407
50	98	75	4	72	2.154989	1.705154	1.28378378	0.51742081
51	1	3	1	32	-1.27742	-1.70895	-1.4189189	-1.2925339
52	32	44	3	40	-0.18047	0.235194	0.38288288	-0.930543
53	1	3	1	57	-1.27742	-1.70895	-1.4189189	-0.1613122
54	58	64	4	100	0.739561	1.183555	1.28378378	1.78438914
55	6	13	1	91	-1.1005	-1.23477	-1.4189189	1.37714932
56	61	67	4	60	0.845718	1.32581	1.28378378	-0.0255656
57	82	71	4	55	1.588818	1.515482	1.28378378	-0.25181
58	2	4	1	68	-1.24204	-1.66153	-1.4189189	0.33642534
59	31	44	3	31	-0.21585	0.235194	0.38288288	-1.3377828
60	49	55	3	53	0.42109	0.756793	0.38288288	-0.3423077
61	37	48	3	31	-0.00354	0.424866	0.38288288	-1.3377828
62	26	41	2	49	-0.39278	0.092939	-0.518018	-0.5233032
63	52	59	4	44	0.527247	0.946465	1.28378378	-0.7495475
64	10	26	2	83	-0.95895	-0.61833	-0.518018	1.01515837
65	28	42	2	96	-0.32201	0.140358	-0.518018	1.60339367
66	10	26	2	86	-0.95895	-0.61833	-0.518018	1.15090498
67	24	40	2	98	-0.46355	0.045521	-0.518018	1.6938914
68	3	8	1	62	-1.20665	-1.47186	-1.4189189	0.06493213
69	23	40	2	58	-0.49894	0.045521	-0.518018	-0.1160633
70	41	50	3	81	0.138004	0.519702	0.38288288	0.92466063
71	32	46	3	91	-0.18047	0.33003	0.38288288	1.37714932
72	50	58	4	26	0.456476	0.899047	1.28378378	-1.5640271
73	38	49	3	57	0.031847	0.472284	0.38288288	-0.1613122
74	14	29	2	34	-0.81741	-0.47608	-0.518018	-1.2020362
75	43	51	3	98	0.208776	0.56712	0.38288288	1.6938914
76	11	28	2	43	-0.92357	-0.5235	-0.518018	-0.7947964
77	38	49	3	33	0.031847	0.472284	0.38288288	-1.2472851
78	15	30	2	37	-0.78202	-0.42866	-0.518018	-1.0662896
79	61	66	4	48	0.845718	1.278392	1.28378378	-0.568552
80	57	64	4	94	0.704176	1.183555	1.28378378	1.51289593
81	55	62	4	25	0.633404	1.088719	1.28378378	-1.609276
82	89	73	4	37	1.836518	1.610318	1.28378378	-1.0662896
83	10	25	2	28	-0.95895	-0.66575	-0.518018	-1.4735294
84	78	69	4	31	1.447275	1.420646	1.28378378	-1.3377828
85	74	69	4	39	1.305732	1.420646	1.28378378	-0.9757919
86	6	13	1	26	-1.1005	-1.23477	-1.4189189	-1.5640271
87	2	4	1	41	-1.24204	-1.66153	-1.4189189	-0.8852941
88	2	6	1	90	-1.24204	-1.56669	-1.4189189	1.33190045
89	99	75	4	74	2.190375	1.705154	1.28378378	0.60791855
90	4	10	1	77	-1.17127	-1.37702	-1.4189189	0.74366516
91	47	53	3	81	0.350318	0.661956	0.38288288	0.92466063
92	90	74	4	39	1.871904	1.657736	1.28378378	-0.9757919
93	56	63	4	76	0.66879	1.136137	1.28378378	0.69841629
94	20	35	2	54	-0.6051	-0.19157	-0.518018	-0.2970588
95	9	19	1	37	-0.99434	-0.95026	-1.4189189	-1.0662896
96	22	38	2	100	-0.53432	-0.04931	-0.518018	1.78438914
97	53	60	4	42	0.562633	0.993883	1.28378378	-0.8400452
98	19	35	2	97	-0.64048	-0.19157	-0.518018	1.64864253
99	46	23	1	29	0.314933	-0.76059	-1.4189189	-1.4282805
100	16	45	3	77	-0.74664	0.282612	0.38288288	0.74366516
101	57	2	2	78	0.704176	-1.75637	-0.518018	0.78891403
102	55	69	2	73	0.633404	1.420646	-0.518018	0.56266968
103	12	21	1	99	-0.88818	-0.85542	-1.4189189	1.73914027
104	54	53	4	42	0.598018	0.661956	1.28378378	-0.8400452
105	71	61	2	51	1.199575	1.041301	-0.518018	-0.4328054
106	10	16	2	15	-0.95895	-1.09251	-0.518018	-2.0617647
107	35	20	4	30	-0.07431	-0.90284	1.28378378	-1.3830317
108	27	17	1	79	-0.3574	-1.04509	-1.4189189	0.8341629
109	26	44	3	59	-0.39278	0.235194	0.38288288	-0.0708145
110	40	53	4	50	0.102619	0.661956	1.28378378	-0.4780543
111	78	9	1	52	1.447275	-1.42444	-1.4189189	-0.3875566
112	21	37	2	82	-0.56971	-0.09673	-0.518018	0.9699095
113	10	54	4	67	-0.95895	0.709375	1.28378378	0.29117647
114	61	61	1	98	0.845718	1.041301	-1.4189189	1.6938914
115	23	67	2	75	-0.49894	1.32581	-0.518018	0.65316742
116	71	60	4	45	1.199575	0.993883	1.28378378	-0.7042986
117	81	39	1	61	1.553432	-0.0019	-1.4189189	0.01968326
118	96	18	4	46	2.084218	-0.99768	1.28378378	-0.6590498
119	126	23	4	70	3.145789	-0.76059	1.28378378	0.42692308
120	49	16	1	85	0.42109	-1.09251	-1.4189189	1.10565611
121	19	8	3	57	-0.64048	-1.47186	0.38288288	-0.1613122
122	73	26	1	63	1.270347	-0.61833	-1.4189189	0.110181
123	61	29	2	49	0.845718	-0.47608	-0.518018	-0.5233032
124	34	19	1	72	-0.1097	-0.95026	-1.4189189	0.51742081
125	8	3	3	45	-1.02972	-1.70895	0.38288288	-0.7042986
126	28	7	3	55	-0.32201	-1.51928	0.38288288	-0.25181
127	44	62	4	49	0.244161	1.088719	1.28378378	-0.5233032
128	58	37	2	31	0.739561	-0.09673	-0.518018	-1.3377828
129	85	6	3	39	1.694975	-1.56669	0.38288288	-0.9757919
130	20	30	4	65	-0.6051	-0.42866	1.28378378	0.20067873
131	87	54	4	94	1.765747	0.709375	1.28378378	1.51289593
132	26	7	2	50	-0.39278	-1.51928	-0.518018	-0.4780543
133	86	31	1	62	1.730361	-0.38124	-1.4189189	0.06493213
134	19	18	4	28	-0.64048	-0.99768	1.28378378	-1.4735294
135	86	13	1	61	1.730361	-1.23477	-1.4189189	0.01968326
136	56	42	3	54	0.66879	0.140358	0.38288288	-0.2970588
137	15	28	4	35	-0.78202	-0.5235	1.28378378	-1.1567873
138	41	36	3	79	0.138004	-0.14415	0.38288288	0.8341629
139	38	45	3	60	0.031847	0.282612	0.38288288	-0.0255656
140	16	30	2	77	-0.74664	-0.42866	-0.518018	0.74366516
141	2	7	1	50	-1.24204	-1.51928	-1.4189189	-0.4780543
142	51	59	4	52	0.491861	0.946465	1.28378378	-0.3875566
143	33	47	3	63	-0.14508	0.377448	0.38288288	0.110181
144	14	28	2	28	-0.81741	-0.5235	-0.518018	-1.4735294
145	72	68	4	72	1.234961	1.373228	1.28378378	0.51742081
146	10	22	2	78	-0.95895	-0.808	-0.518018	0.78891403
147	18	33	2	52	-0.67587	-0.28641	-0.518018	-0.3875566
148	9	20	2	25	-0.99434	-0.90284	-0.518018	-1.609276
149	2	5	1	95	-1.24204	-1.61411	-1.4189189	1.5581448
150	48	54	3	26	0.385704	0.709375	0.38288288	-1.5640271
151	28	43	2	31	-0.32201	0.187776	-0.518018	-1.3377828
152	32	45	3	36	-0.18047	0.282612	0.38288288	-1.1115385
153	20	35	2	73	-0.6051	-0.19157	-0.518018	0.56266968
154	40	50	3	59	0.102619	0.519702	0.38288288	-0.0708145
155	2	6	1	83	-1.24204	-1.56669	-1.4189189	1.01515837
156	49	57	4	84	0.42109	0.851629	1.28378378	1.06040724
157	37	48	3	44	-0.00354	0.424866	0.38288288	-0.7495475
158	86	71	4	36	1.730361	1.515482	1.28378378	-1.1115385
159	9	19	2	59	-0.99434	-0.95026	-0.518018	-0.0708145
160	32	46	3	93	-0.18047	0.33003	0.38288288	1.46764706
161	35	48	3	68	-0.07431	0.424866	0.38288288	0.33642534
162	50	57	4	63	0.456476	0.851629	1.28378378	0.110181
163	2	4	1	41	-1.24204	-1.66153	-1.4189189	-0.8852941
164	13	28	2	38	-0.8528	-0.5235	-0.518018	-1.0210407
165	86	72	4	50	1.730361	1.5629	1.28378378	-0.4780543
166	32	46	3	64	-0.18047	0.33003	0.38288288	0.15542986
167	45	52	3	50	0.279547	0.614538	0.38288288	-0.4780543
168	31	44	3	72	-0.21585	0.235194	0.38288288	0.51742081
169	41	50	3	49	0.138004	0.519702	0.38288288	-0.5233032
170	87	72	4	53	1.765747	1.5629	1.28378378	-0.3423077
171	20	35	2	32	-0.6051	-0.19157	-0.518018	-1.2925339
172	93	74	4	75	1.978061	1.657736	1.28378378	0.65316742
173	22	36	2	32	-0.53432	-0.14415	-0.518018	-1.2925339
174	26	41	2	26	-0.39278	0.092939	-0.518018	-1.5640271
175	29	43	3	64	-0.28662	0.187776	0.38288288	0.15542986
176	67	67	4	93	1.058033	1.32581	1.28378378	1.46764706
177	55	63	4	71	0.633404	1.136137	1.28378378	0.47217195
178	49	56	3	65	0.42109	0.804211	0.38288288	0.20067873
179	59	66	4	32	0.774947	1.278392	1.28378378	-1.2925339
180	52	59	4	63	0.527247	0.946465	1.28378378	0.110181
181	93	74	4	75	1.978061	1.657736	1.28378378	0.65316742
182	16	32	2	89	-0.74664	-0.33382	-0.518018	1.28665158
183	4	9	1	77	-1.17127	-1.42444	-1.4189189	0.74366516
184	18	33	2	31	-0.67587	-0.28641	-0.518018	-1.3377828
185	13	28	2	54	-0.8528	-0.5235	-0.518018	-0.2970588
186	28	42	2	83	-0.32201	0.140358	-0.518018	1.01515837
187	44	52	3	28	0.244161	0.614538	0.38288288	-1.4735294
188	118	19	2	96	2.862703	-0.95026	-0.518018	1.60339367
189	23	39	2	31	-0.49894	-0.0019	-0.518018	-1.3377828
190	23	40	2	30	-0.49894	0.045521	-0.518018	-1.3830317
191	57	64	4	63	0.704176	1.183555	1.28378378	0.110181
192	88	73	4	60	1.801132	1.610318	1.28378378	-0.0255656
193	82	70	4	81	1.588818	1.468064	1.28378378	0.92466063
194	7	16	1	64	-1.06511	-1.09251	-1.4189189	0.15542986
195	7	16	1	63	-1.06511	-1.09251	-1.4189189	0.110181
196	16	31	2	51	-0.74664	-0.38124	-0.518018	-0.4328054
197	37	48	3	93	-0.00354	0.424866	0.38288288	1.46764706
198	50	58	4	76	0.456476	0.899047	1.28378378	0.69841629
199	21	36	2	49	-0.56971	-0.14415	-0.518018	-0.5233032
200	1	2	1	42	-1.27742	-1.75637	-1.4189189	-0.8400452

Only one value of Shift A average Call time corresponding to call center number 119 is greater than 3 hence we say that it is an outlier.

Correlations Correlations AVG SATISFA I AVG NO OF EMPLOYEE SHIFTA AVGSHIFTB AVG CTION LEVE CALL TIME CALL TIMEE 674 SHIFTA AVG_CALL_TIM Pearson Correlation Sig. (2-tailed) 644 039 584 200 044 538 200 .041 200 674 200 800 200 SHIFTB_AVG_CALL TIM Pearson Correlation Sig. (2-tailed) 200 644 200 800 200 AVG SATISFACTION LE Pearson Correlation VEL Sig. (2-tailed) 200 039 584 200 200 044 538 200 200 -.041 200 AVG NO_OF_EMPLOYE Pearson Correlation ES Sig. (2-tailed) 200 200 **. Correlation is significant at the 0.01 level (2-tailed)
We can observe from the correlation table that correlation coefficient between satisfaction level and shift A call times is 0.644 which means that there is moderate positive correlation and satisfaction level increases with increase in Average call times in Shift A

Correlation coefficient between satisfaction level and shift B call times is 0.800 which means that there is strong positive correlation and satisfaction level increases with increase in Average call times in Shift B

Correlation coefficient between satisfaction level and number of employees is -0.041 which means that there is slight negetive correlation and we can say that satisfaction level is not affected by average number of employees