# How to find 1-year population average with intermittent series data

I have performance review data and scores (ranging from 1 to 4) for employees of a company. I need to show the company average over the past year. However, the employees were only ever reviewed for a few weeks in a row at a time.

For example:
Roger was reviewed from Jan 1 through March 1
Steve was reviewed from August 15 through September 15
...etc...

Right now, I'm taking all of the reviews over the year (Jan 1 through Dec 31) and for each day I'm computing the average for that day. I then take all of those days and plot the average score for that day on a line graph with time on the X axis and score on the Y axis.

The problems I'm having are:

• there are gaps of time in these reviews (no one was reviewed in February, 20 people were reviewed in March)
• the higher performing employees may have been reviewed at one part of the year, and the lower performing employees at another
• when I plot this data the average produces a zigzag looking line chart. for example, day 1 the average is 3.4, but day 2 is 1.3. over time this looks like a lot of spikes.

So, where I'm at now is thinking of taking each employee as a "series" (where some series (employees) have data ranging for a few weeks, and some have data ranging a few months) and normalizing them together and computing the average of that normalization.

I'd greatly appreciate any help on this and the best way to present this data!

• Why is time a factor? In other words why would it make a difference that A was reviewed in January and B in August, say? If this doesn't matter than time need not be a complicating factor. Just take average their evaluations by dividing by the number of days scored and take a weighted average based on their sample sizes if the number of days reviewed varies. – Michael R. Chernick Jul 25 '12 at 16:50
• The only reason time was a factor was because I wanted to show how the company was progressing over time. But to answer your question, it doesn't make a difference when they were reviewed. So I think I can just normalize them all without regard to time and average them out that way. – Mike G. Jul 25 '12 at 16:59
• Then at least you can compute it this way each year and look at time trend across years. – Michael R. Chernick Jul 25 '12 at 17:02