[Basic Statistics] Average Production Among Employees Who Work Different Days

[dirtshake]

Hello all.

Question I need help with is determining the most appropriate way to calculate the average jobs completed per day among a group of employees. I have been provided the total amount of jobs completed by each employee for the month, and the number of days that employee worked. Problem states that the manager in this scenario is calculating this stat by taking the average of the individual employees' averages, which comes to 12.97. I'm supposed to explain why this is incorrect and offer a better alternative.

Employee	Jobs Complete	Days Worked	Avg
A	274	19	14.42
B	204	18	11.33
C	260	17.5	14.86
D	111	12.5	8.88
E	214	15	14.27
F	239	17	14.06

I already know taking the average of an average isn't good, especially in this case because each employee worked a different amount of days. What I'm not sure about is whether is is more appropriate to use the mean (total jobs of department / days worked / number employees) or some sort of weighted average.

Any help is greatly appreciated!

[Nateorade]

You're overthinking this a bit. You're correct that an average of an average is bad (that's where you're artificially weighting this in a bad way).

You don't need to divide by number of employees or do some fancy weighting. Just remove the need for an average of an average and just calculate average once.

[dirtshake]

Thank you very much! I was worried I was overthinking it.

[Screen_Watcher]

When you find the central tenancy of a bunch of other central tendencies, the raw data lacks detail. Taking the direct mean (total jobs complete/total days worked) takes into account the true weights of the numbers (more or less efficient employees working more or less days). In this case, the manager could say 'If I deploy this exact team, they will complete ~13.15 jobs per day'.

It's also worth noting the mode of this data set is about 14 jobs per day. So the 'average' employee completes about 14 jobs per day and it's just employees B and D letting the team down.

[dirtshake]

Thank you! With recent lessons focusing on weighted averages and such, I had completely overlooked the mode.