As a manager, an important function to measure performance is to complete a data analysis comparing scores or metrics. While technology makes it possible to easily acquire data, only you can truly understand what it means; and only choosing one or two data points may not show you an accurate picture of what’s happening. Part of your job as an HR manager is to monitor the performance of trainees as they complete a 4-week paid training program, which includes a product knowledge test. You have to determine which trainees can complete the program, which may require remediation (additional training and re-testing), and which should not continue with the training (termination) based on their scores on the product knowledge exam.

Statistics:

- Mean: 75.5
- Standard Deviation: 19.57
- Minimum: 18
- Quartile 1: 67.75
- Median: 80.5
- Quartile 3: 87
- Maximum: 99

Questions:

1. Would you prefer to use the mean or the median in this dataset’s measure of central tendency? Why?

2. Based on this training class’s scores, what scores do you think should be considered for completion, remediation, and termination? How did you come to that conclusion?

3. Do you think that these scores should be the threshold for all training classes? Why or why not?

Trainee Scores:

- Trainee 1: 83
- Trainee 2: 82
- Trainee 3: 18
- Trainee 4: 93
- Trainee 5: 68
- Trainee 6: 96
- Trainee 7: 74
- Trainee 8: 67
- Trainee 9: 93
- Trainee 10: 98
- Trainee 11: 82
- Trainee 12: 62
- Trainee 13: 85
- Trainee 14: 78
- Trainee 15: 64
- Trainee 16: 82
- Trainee 17: 83
- Trainee 18: 93
- Trainee 19: 79
- Trainee 20: 70
- Trainee 21: 27
- Trainee 22: 78
- Trainee 23: 99
- Trainee 24: 58

Given the dataset's measure of central tendency, I would prefer to use the median (80.5) over the mean (75.5) because the median is less affected by extreme scores and outliers, providing a more accurate reflection of central tendency in this context.

Based on the training class's scores, the thresholds for completion, remediation, and termination should be as follows:
Completion: Scores above the median (80.5)
Remediation: Scores between the first quartile (67.75) and the median (80.5)
Termination: Scores below the first quartile (67.75)

Use the median as it is less affected by outliers. Scores above Q3 for completion, between Q1 and Q3 for remediation, and below Q1 for termination.

Central Tendency: When deciding between using the mean or the median, it is important to consider the impact of outliers. In this dataset, since there are extreme values, like trainee 3 with a score of 18, it is better to use the median as a measure of central tendency to avoid being skewed by these outliers. The median is 80.5.

Performance Evaluation: Based on the scores, trainees with scores above Q3 (87) could be considered for completion, those between Q1 (67.75) and Q3 (87) may need remediation, and those below Q1 (67.75) might be considered for termination.

Threshold for Training Classes: Whether these scores should be the threshold for all training classes depends on the specific context of each class. Factors like the difficulty level of the test and the characteristics of the trainees should be considered to determine if these thresholds are appropriate universally.