Assignment:
Management wants to investigate the time it takes to complete a manual assembly task. A sample of 12 workers is timed, yielding the following data (in seconds):
21.3 15.2 13.6 16.1 15.0 19.2 21.0 14.3 15.6 20.1 21.1 22.2
• Find mean and median; do you think that the data are skewed?
• Find the standard deviation.
• What is the percentile rank of the person who took 20.1 seconds to complete the task?
• Find the quartiles, using the second approach that we have described for the calculation of percentiles.
• Suppose that management want to define an acceptable threshold, based on the 90% percentile; all workers taking more than this time are invited to a training session to improve their performance. Find this percentile using the interpolation method.
Provide complete and step by step solution for the question and show calculations and use formulas.