Analysis Of A Bank Branch Located In A Residential Area

Analysis of a Bank Branch Located in a Residential Area's Customer Waiting Time Data

A bank branch situated within a residential community has implemented a new process to improve customer service during the lunch hour from 12:00 P.M. to 1:00 P.M. To evaluate the effectiveness of this process, waiting times (measured in minutes from the moment a customer enters the queue to when they reach the teller) were recorded over one week during this peak period. A random sample of 15 customer waiting times was collected, with the following data points: 9.66, 5.90, 8.02, 5.79, 8.73, 3.82, 8.01, 8.35, 10.49, 6.68, 5.64, 4.08, 6.17, 9.91, and 5.47 minutes.

The tasks are to compute the descriptive statistics (mean, median, first quartile, third quartile), measures of variability (variance, standard deviation, range, interquartile range, coefficient of variation) for this sample of waiting times.

Paper For Above instruction

Understanding customer waiting times and their variability is crucial for evaluating the performance of service processes, especially in high-traffic environments like a bank branch operating in a residential area during peak hours. Efficient management of customer flow not only enhances customer satisfaction but also influences the bank's operational effectiveness and profitability. The analysis of the recorded waiting times provides insights into the process's consistency, responsiveness, and areas requiring improvement. This paper aims to compute key descriptive and variability measures for the given sample data, offering a comprehensive statistical understanding of customer waiting times during this specific period.

Introduction

Customer waiting time is a vital performance indicator in service operations, affecting customer perception, loyalty, and overall service quality. Analyzing this data provides essential insights into the efficiency of the bank's new process during the lunch hour, a critical period with high customer influx. Statistical measures such as the mean, median, quartiles, variance, and others offer a quantitative basis for assessing the process's reliability, consistency, and potential bottlenecks. These metrics serve as a foundation for managerial decisions aiming to optimize customer service experiences and operational workflows.

Data Description and Statistical Computations

The sample consists of 15 waiting time observations: 9.66, 5.90, 8.02, 5.79, 8.73, 3.82, 8.01, 8.35, 10.49, 6.68, 5.64, 4.08, 6.17, 9.91, and 5.47 minutes. Using this data, the following statistical measures are computed:

1. Mean (Average)

The mean provides the average waiting time and is calculated as the sum of all observations divided by the number of observations:

Mean = (Sum of all waiting times) / 15

Sum = 9.66 + 5.90 + 8.02 + 5.79 + 8.73 + 3.82 + 8.01 + 8.35 + 10.49 + 6.68 + 5.64 + 4.08 + 6.17 + 9.91 + 5.47 = 101.75

Mean = 101.75 / 15 ≈ 6.78 minutes

2. Median

Arranging the data in ascending order:

3.82, 4.08, 5.47, 5.64, 5.79, 6.17, 6.68, 8.01, 8.02, 8.35, 8.73, 9.66, 9.91, 10.49

With 15 observations (odd number), the median is the 8th value:

Median = 8.01 minutes

3. First Quartile (Q1)

Q1 corresponds to the 25th percentile, interpolated between the 4th and 5th data points:

Data points for Q1: 4th (5.64) and 5th (5.79)

Q1 = 5.64 + (0.25) (5.79 - 5.64) = 5.64 + 0.25 0.15 = 5.64 + 0.0375 = 5.68 minutes

4. Third Quartile (Q3)

Q3 corresponds to the 75th percentile, interpolated between the 12th and 13th data points:

Data points for Q3: 12th (9.66) and 13th (9.91)

Q3 = 9.66 + (0.75) (9.91 - 9.66) = 9.66 + 0.75 0.25 = 9.66 + 0.1875 = 9.85 minutes

5. Variance

Variance measures the average squared deviation from the mean:

Variance = (Sum of squared deviations) / (n - 1)

Calculating each deviation squared:

  • (9.66 - 6.78)^2 ≈ 8.21
  • (5.90 - 6.78)^2 ≈ 0.77
  • (8.02 - 6.78)^2 ≈ 1.55
  • (5.79 - 6.78)^2 ≈ 0.99
  • (8.73 - 6.78)^2 ≈ 3.83
  • (3.82 - 6.78)^2 ≈ 8.80
  • (8.01 - 6.78)^2 ≈ 1.55
  • (8.35 - 6.78)^2 ≈ 2.75
  • (10.49 - 6.78)^2 ≈ 14.03
  • (6.68 - 6.78)^2 ≈ 0.01
  • (5.64 - 6.78)^2 ≈ 1.28
  • (4.08 - 6.78)^2 ≈ 7.03
  • (6.17 - 6.78)^2 ≈ 0.37
  • (9.91 - 6.78)^2 ≈ 9.09
  • (5.47 - 6.78)^2 ≈ 1.72

Total squared deviations ≈ 65.87

Variance = 65.87 / (15 - 1) ≈ 4.71

6. Standard Deviation

Standard deviation is the square root of variance:

SD ≈ √4.71 ≈ 2.17 minutes

7. Range

The difference between maximum and minimum values:

Range = 10.49 - 3.82 = 6.67 minutes

8. Interquartile Range (IQR)

IQR = Q3 - Q1 = 9.85 - 5.68 = 4.17 minutes

9. Coefficient of Variation (CV)

CV measures relative variability:

CV = (Standard deviation / Mean) × 100 = (2.17 / 6.78) × 100 ≈ 32.02%

Conclusion

The statistical analysis reveals that the average customer waiting time during the peak hour is approximately 6.78 minutes, with a median of 8.01 minutes indicating a slight right-skewed data distribution. The interquartile range of 4.17 minutes shows moderate variability in the middle 50% of waiting times, suggesting some fluctuation around the median. The standard deviation of approximately 2.17 minutes and a coefficient of variation of 32.02% indicate a significant relative variability, which may influence customer satisfaction and perceptions of service efficiency. The range of 6.67 minutes underscores the presence of some customers experiencing considerably longer wait times than others.

By analyzing these metrics, management can determine whether the new process effectively stabilizes waiting times or if further adjustments are needed to improve consistency and reduce customer wait durations.

References

  • Barlow, R. E. (2013). Statistical Methods for Quality Improvement. Pearson.
  • Devore, J. L. (2011). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
  • Montgomery, D. C. (2012). Introduction to Statistical Quality Control. John Wiley & Sons.
  • Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers. Wiley.
  • Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2013). Introduction to Probability and Statistics. Brooks/Cole.
  • Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
  • Weiss, N. A. (2012). Introductory Statistics. Addison-Wesley.
  • Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & Statistics for Engineers & Scientists. Pearson.
  • Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing. Academic Press.
  • Yates, G. (2014). Practical Statistical Process Control. Chapman and Hall/CRC.

Related Assignments