# Calculating average of averages in absence of complete data

I have a dataset with three variables:

Cust_ID   AvgSpend   Location
1         10         A
2         200        A
3         140        B
4         250        B
5         40         C
6         60         C
7         90         D

1. A customer's ID,
2. The customer's average spend
3. Location of the customer

I only have these data, and I have been asked to calculate the average spend at each location. As far as I know, taking the average of Avg Spend here isn't going to be accurate.

Do I need to ask for more data to calculate this?
If I am not provided more data, is there any way to calculate the average spend at each location that I am not aware of?

Elaboration: A business team is interested in getting a rough idea of how much a customer spends typically, at their locations.
Hope this helps, because this is really all I have been informed of by our respected business users.

Thanks.

• Actually, it depends on your precise definition of "average"... Maybe you can try to elaborate your question? – Stefan Mar 7 '16 at 9:37
• @Stefan thank you for your comment. I need to show this to business users, actually, who need it only to get a rough idea of how much money is being spent by a customer at each location. – info_seeker Mar 7 '16 at 9:42
• The ranges of values indeed indicate huge spread and the averages will be quasi meaningless. Ask for more data or warn about inaccuracy. – Yves Daoust Mar 7 '16 at 9:44
• Your title is not related to the question ! – Yves Daoust Mar 7 '16 at 9:45
• You can't further simplify this small dataset without skewing it. Just showing it as it is would probably be the best solution. – Bobson Dugnutt Mar 7 '16 at 9:57

Here is a partial, negative answer:

Without additional information there is no hope to answer your question. Let us only consider one location with $100$ customers - let's label them $\#1, \ldots, \#100$. Customer $\#1$ spends on average $\$1$and customers$\#2, \ldots, \#100$each spend$\$100$ on average.

Consider two scenarios:

In scenario $X$ the costumer $\#1$ is a regular and he visited our location $900$ times in our data set. Costumers $\#2, \ldots, \#100$ each visited only once. Their total spendings are $\$900 + \$990 = \$1890$in$1000$visits. We thus should expect an average spend of$\$18.90$ per visit.

In scenario $Y$ each costumer visited our location $10$ times. Their total spendings are thus $10 \cdot (\$1 + 99 \cdot \$100) = \$9910$which yields an average of$\$99.10$ per visit.

With the data you seem to have available, these scenarios are indistinguishable...

Since you seem to be interested in real life applications rather than made up scenarios, there might still be some hope. For example, you might be able to take data of similar locations into consideration which would allow you to guess some additional information.

• @info_seekeR You're welcome. – Stefan Mar 7 '16 at 10:38