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. Choosing only one or two data points may not provide 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.

Review the mean, standard deviation, and 5-number summary of the trainees’ exam scores below. You can also review the individual exam scores and functions used to calculate the descriptive analyses in Excel, if desired.

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

Respond to the following:

1. Would you prefer to use the mean or the median as 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?

To evaluate the central tendency of the dataset presented, we can consider both the mean and the median. However, choosing the appropriate measure depends on the distribution of the data.

Mean vs. Median:
- The mean of the exam scores is 75.5, and the median is 80.5. The presence of a low minimum score of 18 and a relatively high maximum of 99 indicates potential outliers that could skew the mean.
- In the presence of outliers or skewed data, the median is generally a more reliable measure of central tendency because it splits the data into two equal halves and is not affected by extreme scores. Therefore, I would prefer to use the median as it may better represent the typical trainee's performance in this dataset.
Determining Completion, Remediation, and Termination:
- Completion: Trainees who score above the third quartile (87) can confidently be considered for completion without any remediation, as they are performing above most of their peers.
- Remediation: Trainees scoring between the first quartile (67.75) and the third quartile (87) may require additional training based on specific areas where their knowledge may be lacking.
- Termination: Scores below the first quartile (67.75), particularly near the minimum (18), suggest these trainees might struggle with the required knowledge, indicating potential termination unless further factors justify giving them another opportunity.
Threshold Consistency Across Training Classes:
- It's important to consider whether these thresholds should be applied universally to all training classes. Different batches of trainees might have varying backgrounds and abilities, which could lead to different score distributions.
- Therefore, it would be advisable to calibrate these thresholds based on each specific class's overall performance and characteristics to ensure fairness and relevance. Regular assessment and adjustment based on each cohort's scores can provide a more equitable framework for decision-making.

Overall, using the median provides a more accurate representation of central tendency for making informed decisions, particularly when data may contain outliers or significant variations.