# Response time - what is the best central tendency measure?

#### Broxigar

##### New Member
I have a bunch of people working under me. I give them some tasks to complete on a regular basis. Some of the tasks are time bound and some aren't.

I want to find a "measure" that best captures the response time of each employee. Finally based on this measure I want to see who is the best and worst in terms of response time.

Case 3 is the actual scenario that I want to solve, but if that't not possible I am happy to settle for Case 1 and Case 2.

Below is the data for a user named say Alex.

Code:
+--------------------+-----------+-------------------+
|        Date        | Task name | Time Taken (days) |
+--------------------+-----------+-------------------+
| 1-Jan              | A         | 3                 |
| 8-Jan              | B         | 10                |
| 23-Jan             | C         | 2                 |
| 23-Jan             | D         | 4                 |
| 23-Jan             | E         | 6                 |
| 1-Feb              | F         | 4                 |
| 2-Feb              | G         | 5                 |
| 2-Feb              | H         | 10                |
| Avg. Response time |           | 5.5               |
+--------------------+-----------+-------------------+
I calculated average time taken to complete all the 8 tasks and considered it as the best central tendency measure for response time.

But, I would like to know if there are any statistically robust methods to measure response time where there are no deadlines. I am sure there are..

Code:
+--------+-----------+------------+------------+------------+
|  Date  | Task Name | Time given | Time Taken | % utilized |
+--------+-----------+------------+------------+------------+
| 1-Jan  | A         |          7 |          3 | 43%        |
| 8-Jan  | B         |         14 |         10 | 71%        |
| 23-Jan | C         |          7 |          2 | 29%        |
| 23-Jan | D         |          7 |          4 | 51%        |
| 23-Jan | E         |          7 |          6 | 86%        |
| 1-Feb  | F         |          7 |          4 | 57%        |
| 2-Feb  | G         |          7 |          5 | 71%        |
| 2-Feb  | H         |         14 |         10 | 71%        |
| Avg.   |           |            |            | 61%        |
+--------+-----------+------------+------------+------------+
When there are deadlines I am using Average % of time utilized. Ex: For Task A, Alex was given 7 days time but he completed it in 3 days. So he utilized only 43% of the given time. Lower the better. Overall I have taken average % of time utilized as the central tendency for Alex's response time. Again, here I am taking simple average.

I would like to know if there are any statistically robust methods to measure response time given there are deadlines.

Case 3: Deadlines - Yes / No

Code:
+--------+-----------+------------+------------+------------+
|  Date  | Task Name | Time given | Time Taken | % utilized |
+--------+-----------+------------+------------+------------+
| 1-Jan  | A         | 7          | 3          | 43%        |
| 8-Jan  | B         | 14         | 10         | 71%        |
| 23-Jan | C         | 7          | 2          | 29%        |
| 23-Jan | D         | 7          | 4          | 57%        |
| 23-Jan | E         | 7          | 6          | 86%        |
| 1-Feb  | F         | NA         | 4          | NA         |
| 2-Feb  | G         | NA         | 5          | NA         |
| 2-Feb  | H         | NA         | 10         | NA         |
| Avg.   |           |            | 5.5        |            |
+--------+-----------+------------+------------+------------+
This is actually the case in real. Here I am clueless on how to find a central tendency when there are tasks both with & without deadlines.

Drawbacks: Few points I have missed and should ideally be considered.

1. How should I deal withe data where are multiple tasks assigned on a given day?

For Ex: 1st Jan and 8th Jan he was given only 1 tasks. But on 23rd Jan he was given 3 tasks. Between 23rd Jan and 30th Jan he has to complete 3 tasks.

"Average" as a central tendency ignores that there a 3 tasks given on the same day and calculates average thinking that it's linear data but actually it's not linear data.

Alex's response time is much better than what "average" indicates as it doesn't recognize that Alex was give 3 tasks one the same day. even though Task c, D and E have 7 days time but realistically these have roughly 2 days each to complete.

2. How to deal with data where there are overlaps?

Assume Task F and Task G should be completed within 7 days.

though tasks F and G are given on two different days, they overlap. Task F is to be done between 1st and 7th Feb, Task G between 2nd and 8th Feb. 2nd to 7th Feb is common for both the tasks. He is expect to completed two tasks is 8 days.

So considering Case 3 and the drawbacks (1 and 2), what are some better measures of response time?

thank you.

#### Karabiner

##### TS Contributor
Have you considered using the median?

With Kind regards

K.

#### Broxigar

##### New Member
Have you considered using the median?

With Kind regards

K.
the real question here is when there are tasks which has both with and without deadlines, how do you deal with it?

at the end i have to give just one single figure that describes that user's response time in general.