I have a table of daily events for a number of locations that I am trying to summarize for a week. For a weekly summary, are both of these methods correct, and how would they be interpreted?
- SUM(Events)/SUM(Loc. Count) = 8.63 | Interpretation: For each location during the week, there was an average of 8.63 events.
- Sum(Events per Loc. Count) = 60 | Interpretation: ???
Table
| Date | Day | Loc. Count | Events | Events per Loc. Count|
|-----------|-----|------------|--------|----------------------|
| 6/11/2018 | Mon | 200 | 1,100 | 5.5 |
| 6/12/2018 | Tue | 198 | 1,550 | 7.8 |
| 6/13/2018 | Wed | 197 | 1,425 | 7.2 |
| 6/14/2018 | Thu | 202 | 3,400 | 16.8 |
| 6/15/2018 | Fri | 205 | 2,800 | 13.7 |
| 6/16/2018 | Sat | 207 | 1,200 | 5.8 |
| 6/17/2018 | Sun | 190 | 600 | 3.2 |
| Method 1 | | 1,399 | 12,075 | 8.63 (12,075/1,399) |
| Method 2 | | 1,399 | 12,075 | 60 (5.5+7.8+7.2...) |
1) SUM(Events)/SUM(Loc. Count) = 8.63 | Interpretation: For each location during the week, there was an average of 8.63 events.
That is the correct interpretation. Is it useful. Probably. It tells us how many events in general to expect given a number of locations.
2) Sum(Events per Loc. Count) = 60 | Interpretation: ???
The sum of the event/location ratios. (Is it useful? That's not for me to say. It could be to someone.)
3) Sum(Events per Loc. Count)/Count = 8.57
Interpretation: The average of the event/locations ratios. Is it useful? To some people maybe. (For gamblers making book, definitely.) Is the same and the average number of events over for each location? No. It is not. Should it be interpreted as such? No. Not at all. It should not. But is it useless. That depends.
...
An analogy is comparing a player who is good because he scores a lot (method 1) vs. a player who is good because he wins a lot of games (method 2 and 3). They are not the same thing.