Sample Report and Solution to
Quality Scores at ABAZ
Prepared by: Dr. Mike Bendixen
Dr. Cynthia Ruppel
Date: June 29, 2009
Nova Southeastern University
H. Wayne Huizenga School
of Business & Entrepreneurship
Assignment for Course:  QNT5040 
Submitted to:  Dr. M Bendixen 
Submitted by:  Cindy Ruppel 
N000999999  
3301 College Ave
Davie, FL33314 

9545555555  
9545550000 
Date of Submission: June 29, 2009
Title of Assignment: Quality Scores at ABAZ
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Management Report for Quality Scores at ABAZ
Executive Summary
ABAZ is seeking an accurate and easy way to monitor the quality performance of the Customer Service Agents (CSRs) in its call center. One quality monitoring option, control charts, requires that the data be normally distributed. Tests were conducted on a random sample of quality data that was collected to determine if it meets this requirement.
After completing several types of analysis, both numerical and visual, it can be concluded that the data is not normally distributed. Thus, this dataset should not be used to construct control charts without taking steps to either find a method to normalize the data, if possible, or another method of quality assessment and monitoring should be used.
Background
Since Customer Service Representatives (CSRs) often represent the bank to our customers, it is important that this interaction is of high quality for the purposes of customer satisfaction and retention. Thus, ABAZ would like to asses and monitor the quality of calls completed by CSRs in our call center. Quality data was randomly collected for five CSRs over a 12 month period. The quality score of the call was assessed by quality control monitors applying the standards the bank wishes to uphold. It can be assumed that it is important for proper measures to be used and applied fairly, since quarterly bonuses are based on these assessments.
This report is designed to determine if a control chart is an appropriate way to measure quality. Properly developed control charts can provide information that is the basis for action such as disciplining a CSR, giving a CSR a bonus, providing additional training to a specific CSR, etc. The information provided by a control chart is:
1) the basic variability of the quality characteristic,
2) consistency of performance, and
3) average level of the quality characteristic (Grant & Leavenworth, 1996).
Problem
Is the quality data collected normally distributed so that it can be used to develop quality control charts for the assessment of CSRs in ABAZ’s call center?
Analysis
Since the data was collected randomly and in a sufficiently large sample size it is appropriate for use in quality control charts if it is normally distributed. Control charts are designed to separate normal variation (since some variability is unavoidable since different human beings are involved with different issues) from abnormal variation (variation beyond acceptable or “normal” limits), so that abnormal variation can be dealt with appropriately. Note in a normal distribution, or bell shaped curve, some calls will have scores above the mean and some will have quality scores below the mean. Thus it is important that the data be normally distributed to be used to construct the chart and identify what levels of variation are normal. “Serious mistakes often are made when it is assumed that the distribution of an industrial quality characteristic is normal” (Grant & Leavenworth, p.103).
In order to examine the distribution of quality scores, the entire sample of 300 data points was analyzed (5 scores/month/CSR x 12 months x 5 CSRs). Descriptive statistics were computed in Microsoft Office Excel 2007 (refer Appendix 1) and these are summarized in Table 1.
From these statistics it can be seen that the mean is less than the median which is less than the mode. This is a clear indication of a negative skew in the data, confirmed by a negative value of the coefficient of skewness. This is in sharp contrast to a normal distribution which is perfectly symmetrical.
Table 1: Summary of Descriptive Statistics

Measure
Value
Mean 91.28
Median 93.98
Mode 100.00
Standard Deviation 8.29
Variance 68.75
Coefficient of Variation 9.08%
Max 100.00
Min 34.34
Range 65.66
25th percentile 86.79
50th percentile 93.98
75th percentile 97.25
Interquartile Range 10.46
Skew 1.69
Excess kurtosis 6.68
A normal distribution has a skewness and excess kurtosis both equal to zero. However, measures for this data indicate that the data follows a negative skewed leptokurtic distribution.
Scott’s rule (Hyndman, 1995) was used to calculate the optimal bin width for constructing a picture of the data called a histogram of the data. An optimal value of 4.34 was determined but, for practical purposes, a bin width of 5.00 was used as this is a common counting multiple. A histogram of the data is illustrated in Figure 1. Again it is apparent from this graph of the data that the distribution of the data is skewed and does not resemble a normal distribution.
Conclusions and Recommendations
It is apparent from the analysis that quality scores, as currently assessed at ABAZ, are not normally distributed. This implies that the assumption of normally distributed data for the use of control charts will be violated and this should be avoided. Should ABAZ wish to use control charts, alternative methods of quality assessment should be considered.
Figure 1: Histogram of Data
Bibliography
Bendixen, M. (2009). Quality scores at ABAZ. Fort Lauderdale, FL: Nova Southeastern University.
Grant, E. L., & Leavenworth, R. S. (1996). Statistical Quality Control (7th ed.). Boston: WCB/McGrawHill.
Hyndman, R. J. (1995). The problem with Sturges’ rule for constructing histograms. Retrieved June 27, 2009, from http://wwwpersonal.buseco.monash.edu.au/~hyndman/papers/sturges.htm
Kros, J. F. (2008). Spreadsheet modeling for business decisions. New York: McGrawHill/Irwin.
Microsoft Office Excel. (2007). Redmond, WA: Microsoft Corporation.
Appendix 1