Question

Using the Quality Summary and Call Center Data, provide a summary report for the vice president including the following information in an essay with a minimum of 500 words:

1. List the relative frequency for overall type of calls, call quality, and call errors.
2. Provide descriptive statistics for call time to include the mean, median, mode, variance, standard deviation, and range.
3. Provide the following probabilities:
   1. CLM Error and AM Shift
   2. COV Error and PM Shift
   3. SAV Error or AM Shift
   4. Given that the call comes in the morning, what is the probability of a CLM Error?
4. Based on the data, which error(s) should the team focus on? Does shift matter? Explain your answers.
5. Evaluate the current call time if customers expect to have their calls handled within approximately 7.5 minutes on the phone.

Overall Incoming Calls by Type	Frequency			Call Quality	Frequency		Call Errors	Frequency
Check coverage of policy	25625			Correct	850		Incorrect coverage quote  (COV)	54
Check status of claim	22654			Incorrect	150		Incorrect capture of claim  (CLM)	42
Update address	18723						Did not transfer to "Save a Policy" (SAV)	32
File a claim	13499						Incorrect claim status provided  (STAT)	22
Update information on claim	6200
Update Policy	5126
Cancel Policy	3842

Call Time	Reason	Shift
6.50	STAT	AM
6.50	STAT	AM
6.50	STAT	AM
6.50	STAT	AM
7.00	SAV	AM
7.00	COV	AM
7.00	COV	AM
7.00	COV	AM
7.00	COV	AM
8.00	COV	AM
8.00	COV	AM
8.50	SAV	AM
8.50	SAV	AM
9.00	SAV	AM
9.00	SAV	AM
9.00	COV	AM
9.00	COV	AM
9.50	COV	AM
9.50	CLM	AM
9.50	CLM	AM
10.00	COV	AM
10.00	COV	AM
10.00	COV	AM
10.00	COV	AM
10.00	COV	AM
10.50	CLM	AM
10.50	CLM	AM
10.50	CLM	AM
10.50	CLM	AM
10.50	CLM	AM
10.50	CLM	AM
10.50	CLM	AM
10.50	SAV	AM
11.50	SAV	AM
11.50	SAV	AM
11.50	SAV	AM
12.00	CLM	AM
12.00	CLM	AM
12.00	CLM	AM
12.00	CLM	AM
12.50	CLM	AM
12.50	CLM	AM
13.00	COV	AM
13.00	SAV	AM
13.50	COV	AM
15.50	COV	AM
16.00	COV	AM
16.50	SAV	AM
17.00	COV	AM
18.00	COV	AM
6.00	COV	PM
9.00	COV	PM
9.50	COV	PM
10.00	SAV	PM
10.50	COV	PM
10.50	COV	PM
11.00	CLM	PM
11.00	CLM	PM
11.00	COV	PM
11.00	COV	PM
11.50	COV	PM
11.50	COV	PM
11.50	COV	PM
12.00	COV	PM
12.00	COV	PM
12.00	STAT	PM
12.00	STAT	PM
12.00	STAT	PM
12.00	STAT	PM
12.00	STAT	PM
12.50	CLM	PM
12.50	CLM	PM
12.50	CLM	PM
12.50	CLM	PM
13.00	CLM	PM
13.00	CLM	PM
13.50	CLM	PM
13.50	CLM	PM
14.00	COV	PM
14.00	SAV	PM
14.00	COV	PM
14.00	CLM	PM
14.00	COV	PM
14.50	CLM	PM
14.50	COV	PM
14.50	CLM	PM
15.00	CLM	PM
15.00	CLM	PM
15.50	CLM	PM
16.00	CLM	PM
16.50	CLM	PM
17.00	COV	PM
17.50	COV	PM
18.00	SAV	PM
18.00	SAV	PM
18.00	COV	PM
18.50	SAV	PM
19.00	COV	PM
19.50	COV	PM
19.50	COV	PM
5.25	STAT	AM
5.25	STAT	PM
5.25	STAT	AM
5.25	STAT	PM
5.75	STAT	AM
5.75	STAT	PM
5.75	STAT	AM
5.75	STAT	PM
5.75	STAT	AM
6.75	STAT	PM
6.75	STAT	AM
7.25	SAV	PM
7.25	SAV	AM
7.75	SAV	PM
7.75	SAV	AM
7.75	CLM	PM
7.75	CLM	AM
8.25	CLM	PM
8.25	CLM	AM
8.25	CLM	PM
8.75	CLM	AM
8.75	COV	PM
8.75	COV	AM
8.75	SAV	PM
8.75	SAV	AM
9.25	SAV	PM
9.25	SAV	AM
9.25	CLM	PM
9.25	COV	AM
9.25	STAT	PM
9.25	CLM	AM
9.25	COV	PM
9.25	SAV	AM
10.25	STAT	PM
10.25	COV	AM
10.25	SAV	PM
10.75	COV	AM
10.75	COV	PM
10.75	SAV	AM
10.75	COV	PM
11.25	COV	AM
11.25	COV	PM
11.75	SAV	AM
11.75	COV	PM
12.25	COV	AM
14.25	CLM	PM
14.75	SAV	AM
15.25	SAV	PM
15.75	SAV	AM
16.75	SAV	PM

Answer 1

Part 1: Relative Frequency

The relative frequencies for each frequency table is obtained below,

1. Incoming Calls by Type

The relative frequencies for Incoming Calls by Types are obtained using the formula,

Overall Incoming Calls by Type	Frequency	Relative Frequency
Check coverage of policy	25625	25625/95669=0.2679
Check status of claim	22654	22654/95669=0.2368
Update address	18723	18723/95669=0.1957
File a claim	13499	13499/95669=0.1411
Update information on claim	6200	6200/95669=0.0648
Update Policy	5126	5126/95669=0.0536
Cancel Policy	3842	3842/95669=0.0402
Total	95669	1

2. Call Quality

Call Quality	Frequency	Relative Frequency
Correct	850	850/1000=0.8500
Incorrect	150	150/1000=0.1500
Total	1000	1

3. Call Errors

Call Errors	Frequency	Relative Frequency
Incorrect coverage quote  (COV)	54	54/150=0.3600
Incorrect capture of claim  (CLM)	42	42/150=0.2800
Did not transfer to "Save a Policy" (SAV)	32	32/150=0.2133
Incorrect claim status provided  (STAT)	22	22/150=0.1467
Total	150	1

Part 2 Descriptive Statistic

The descriptive statistic for Call Time is obtained in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Descriptive Statistic. The screenshot is shown below,

Step 1: Input Range: Call Time column, Grouped By: Columns, tick Summary Statistic. The screenshot is shown below,

The result is obtained.

The mean, median, mode, variance, standard deviation, and range of the call time data are,

Call Time
Mean	11.06666667
Median	10.625
Mode	12
Standard Deviation	3.383693956
Sample Variance	11.44938479
Range	14.25

Part 3 The probabilities

To calculate the desired probabilities first sort the call time data values and Reason by Shift in AM and PM by following the this step in excel.

Step 1: Select all the data values then DATA > Sort > Sort by: Shift, Sort On: Values, Order: A to Z. The screenshot is shown below,

The result is obtained. For ease of calculation in excel, separate all the data by AM and PM shift in different columns.

1. CLM Error and AM Shift

The probability for CLM Error and AM Shift is obtained by first count the Total AM shift and count the CLM error in AM shift in excel. The screenshot is shown below,

2. COV Error and PM Shift

The probability for COV Error and PM Shift is obtained by first count the Total AM shift and count the CLM error in AM shift in excel. The screenshot is shown below,

3. SAV Error or AM Shift

4.

Using the conditional probability law,

Part 4: Conclusion:

1. Based on the data,

AM Shift
	Count	Probability
STAT	10	0.1333333
SAV	20	0.2666667
COV	26	0.3466667
CLM	19	0.2533333

PM Shift
	Count	Probability
STAT	12	0.16
SAV	12	0.16
COV	28	0.373333333
CLM	23	0.306666667

We can see that COV error is large in both of the shift hence we need to focus more on COV error.

And the difference in probabilities of errors type occurs in the shifts hence shift matters.

2.

Sort the Call Time data by Call Time Smallest to Largest. The screenshot is shown below,

Call Time	Reason	Shift
5.25	STAT	AM		Total Call Time within 7.5 minutes	23
5.25	STAT	PM
5.25	STAT	AM
5.25	STAT	PM		Reason
5.75	STAT	AM			Count	Probability
5.75	STAT	PM		STAT	15	0.6521739
5.75	STAT	AM		SAV	3	0.1304348
5.75	STAT	PM		COV	5	0.2173913
5.75	STAT	AM		CLM	0	0
6	COV	PM
6.5	STAT	AM		Shift
6.5	STAT	AM			Count	Probability
6.5	STAT	AM		AM	16	0.6956522
6.5	STAT	AM		PM	7	0.3043478
6.75	STAT	PM
6.75	STAT	AM
7	SAV	AM
7	COV	AM
7	COV	AM
7	COV	AM
7	COV	AM
7.25	SAV	PM
7.25	SAV	AM

Evaluation:

STAT error is large followed by COV error

Probability of call in AM shift is large