# Help coming with a descriptive statistic

I have some data about employee performance that I want to create a descriptive statistic for that can easily show at a glance how efficient the employee is.

Let's start with some sample data: (The process times are in seconds)

+----------+------------------+--------------+--------------+--------------+
| Employee | Avg Process Time |  Store Avg   | Buys Per Day | Total # Buys |
+----------+------------------+--------------+--------------+--------------+
| 1        | 291              | 376.8        | 4.4          | 22           |
+----------+------------------+--------------+--------------+--------------+
| 2        | 874              | 376.8        | 4            | 4            |
+----------+------------------+--------------+--------------+--------------+
| 3        | 291              | 376.8        | 2.5          | 10           |
+----------+------------------+--------------+--------------+--------------+
| 4        | 294              | 376.8        | 8            | 160          |
+----------+------------------+--------------+--------------+--------------+
| 5        | 1331             | 376.8        | 1            | 1            |
+----------+------------------+--------------+--------------+--------------+
| 6        | 284              | 376.8        | 3            | 42           |
+----------+------------------+--------------+--------------+--------------+
| 7        | 537              | 376.8        | 4.8          | 19           |
+----------+------------------+--------------+--------------+--------------+
| 8        | 354              | 376.8        | 8.7          | 78           |
+----------+------------------+--------------+--------------+--------------+
| 9        | 453              | 376.8        | 6.2          | 131          |
+----------+------------------+--------------+--------------+--------------+
| 10       | 299              | 376.8        | 2.6          | 26           |
+----------+------------------+--------------+--------------+--------------+
| 11       | 438              | 376.8        | 7.2          | 123          |
+----------+------------------+--------------+--------------+--------------+


So I want to come up with one descriptive statistic that shows how effective this employee is relative to the store average. Obviously lower times are better. I also want to factor in the amount of buys that they worked, and compensate for outliers like employee #5. I'd really like to get to a number that lies from 0-100 with 100 being the most efficient employee.

Can someone point me in the right direction for my research? I'm not looking for someone to write a formula for me necessarily. I just don't necessarily know how I should approach it.

Thanks!

EDIT:

Okay here is the way I am displaying the data right now. Those little bullet graphs on the right are useful for showing how each employee performs against the store average. What I want to add is a single number that takes the 'idea' of those graphs and takes into account the number of 'buys' (transactions) as well.

(PT is process time, PT/C is process time per container(bin). Each 'buy' or transaction can have one or more 'bins' and more 'bins' usually means more process time)

• Do you mean "effective" or "efficient"? In either case, the task is to develop a quantitative combination of the data you have that best expresses or measures what you have in mind. – whuber Mar 22 '16 at 17:26
• Yeah I suppose effective is a better word. Can you point me in the right direction on how I would start to think about doing this? – Ryan VanVuren Mar 22 '16 at 17:33
• Can you add some context around "buys"? Specifically, is working more buys better? Do you have an idea if either process time or buys should be given more weight in the metric? – dnbwise Mar 22 '16 at 17:33
• Clicking on the valuation tag will produce a list of related threads. Many are of poor quality because the original questions contained insufficient information to allow for objective or focused answers, but you may find the occasional answer--and perhaps many of the comments--to be of some use. – whuber Mar 22 '16 at 17:38
• @dnbwise A 'buy' is basically one transaction. I definitely want to place an emphasis on the employees who are able to stay at or below the store average while having higher total 'buy' counts. – Ryan VanVuren Mar 22 '16 at 18:45

You could find the relative ranking of factors using z-scores or use the IQR in order to compare those in each observation, then create a composite score.

Here is an example considering average time and total buys with equal weight. I have calculated the z-score of each factor, found where they fall in the distribution (here, I am assuming normal), and created a composite (i.e. $(p_t + p_b)/ 2$). The interpretation of the composite is that an average worker will be at .5, a worker above or below that number is respectively more or less "efficient".

+-----+-----+-----+-----+-----+-----+-----+
|     |buys |z    |     |     |     |     |
+-----+-----+-----+-----+-----+-----+-----+
|291  |22   |-0.65|-0.62|0.74 |0.27 |0.51 |
+-----+-----+-----+-----+-----+-----+-----+
|874  |4    |1.21 |-0.95|0.11 |0.17 |0.14 |
+-----+-----+-----+-----+-----+-----+-----+
|291  |10   |-0.65|-0.84|0.74 |0.20 |0.47 |
+-----+-----+-----+-----+-----+-----+-----+
|294  |160  |-0.64| 1.90|0.74 |0.97 |0.86 |
+-----+-----+-----+-----+-----+-----+-----+
|1331 |1    |2.67 |-1.01|0.00 |0.16 |0.08 |
+-----+-----+-----+-----+-----+-----+-----+
|284  |42   |-0.68|-0.26|0.75 |0.40 |0.57 |
+-----+-----+-----+-----+-----+-----+-----+
|537  |19   |0.13 |-0.68|0.45 |0.25 |0.35 |
+-----+-----+-----+-----+-----+-----+-----+
|354  |78   |-0.45|0.40 |0.67 |0.66 |0.67 |
+-----+-----+-----+-----+-----+-----+-----+
|453  |131  |-0.13|1.37 |0.55 |0.91 |0.73 |
+-----+-----+-----+-----+-----+-----+-----+
|299  |26   |-0.63|-0.55|0.73 |0.29 |0.51 |
+-----+-----+-----+-----+-----+-----+-----+
|438  |123  |-0.18|1.23 |0.57 |0.89 |0.73 |
+-----+-----+-----+-----+-----+-----+-----+

• Thank you @dnbwise, this is exactly what I was looking for as a starting point. – Ryan VanVuren Mar 29 '16 at 1:15