# Aggregation system for percentage Key Performance Indicators (KPIs)

I need some suggestions for an issue regarding our business intelligence (BI) system, percentage Key Performance Indicators (KPIs) and average values.
I am using a BI system for our organization, which allows for quantitative four-monthly KPIs, monitoring individual variation between target and actual values, and producing a four-monthly and yearly percentage.
The only fields our offices have to fill in are, at the beginning of the year, the four-monthly target values, and during the year, the fourth-monthly actual value every four months.
The BI system automatically does all the calculations for the differences and the four-monthly and total percentage of success.

For instance:

KPI "Clients" | Target | Actual | Difference | %
---------------------------------------------------
April          4        4         0           100%
August         4        3        -1           75%
December       4        1        -3           25%
---------------------------------------------------
YEARLY TOTAL   12       8        -4           66%


We have to develop a way to extend this to the use of percentage KPI values, keeping the same system (only target and actual values are to be entered by our offices).
I am having quite a hard time figuring it out, in particular for the yearly totals and success percentage aggregation method. Here is an example:

KPI "% of
reports
delivered
on time"    | Target | Actual | Difference | %
---------------------------------------------------
April          25%       20%       -5        80%
August         50%       55%       +5        100%
December       75%       70%       -5        93,33%
---------------------------------------------------
YEARLY TOTAL   ??%       ??%       ??        ??%


The software engineer proposed to use arithmetic averages, but I know it is wrong to simply average percentages in this way. Also, a percentage yearly final value, in the previous example, would be the december value (75%), not an average value, since it's the final target I am trying to achieve...

Some solutions I've been thinking about:

• using the geometric mean instead of the arithmetic mean, which fits best comparing different items such as percentages, but I am worried about our offices not understanding the resulting yearly total values;
• using a "fixed" yearly target value for all the four-monthly periods (instead of variable four-monthly target values), that would make it easy to measure the differences against the same value, and to average the results.