Question

In: Statistics and Probability

Using the Quality Summary and Call Center Data, provide a summary report for the vice president...

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

Solutions

Expert Solution

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

orchestra answered 2 years ago
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