What is a tone profile?

I'm a public relations researcher. I tell my clients (large corporations) about their profile in the media. This research has a quantitative side which looks at the number of people reached by their PR communications, and a qualitative side which examines how well they have been received - for example, positive, neutral, negative. The latter is what I mean by tone profile. My clients set KPIs based on how much positive or negative coverage they expect to receive for a given period of time, and in what proportions. Thus a company might expect to receive 10% negative coverage in a quarter, and over time this might be a typical score. Occasionally however a single issue might capture the media's attention and suddenly this figure might jump to 30% or 40%. If I was to recommend a KPI for negative coverage based on arithmetic mean over time it might be too high due to inflated scores during certain periods of trouble. Today though I was reading about harmonic mean and I thought this might help me set a KPI range for negative coverage. Thus the upper range would be the arithmetic mean and the lower range would be the harmonic mean, but I don't know if this is sound. Most of the examples I have read about harmonic mean relate to creating averages of rates (such as the speed a car is travelling at over a journey). The reason I thought a harmonic mean might be applicable in this case is that is serves to down-weight the effect of large outliers in the data, while also up-weighting the lower numbers.
I must stress though I am not a statistician or a mathematician, so I don't know if the harmonic mean would be applicable in this case.

You can use both - the arithmetic mean is the correct one to use in this case, but yes, the harmonic mean will give you an alternative view with less outliers influence. As long as you are consistent in tracking both over time it won't hurt.

I guess what I'm trying to say is that the arithmetic mean is the one which will give you the more accurate representation of current status, but the harmonic can be used to better assess longer-term trends by reducing the outlier effect.

Pickup a copy of minitab and run some of the statistical graphs and analyses that it includes. While it is designed for process control, then stats are the same as you are wanting to see and will help to project what you can expect. You can also use it to trend future results against the old results based on changes to the PR approach and the KPIs.

Thank you to both Ivo_ivanov and Draugnar. My client asked for an upper range and a lower range: I have done a little reading and these two methods would seem to provide some consistent method for answering this quesiton. I think.
I have just a couple of questions though.
Firstly Ivo_ivanov, what is your background that you understand the difference between arithmetic mean and harmonic mean? Do you work with stats?
Draugnar, thanks for suggesting mintab. I have been reading about it and I shall investigate further. From your posts I have the impression that you are a programmer. Have you had much experience with statistical software. I actually work for a market research company and my market research colleagues use programs like SPSS. I work in a small division of the company involved with PR research and our methods of data analysis are far less sophisticated. I use Excel and some in-house software (mainly content analysis and media database software and some charting programs). Alas I don't have a background in stats, but I wish I did. I feel we probably need to develop a more sophisticated approach than we currently have.
My client asked for an upper range and a lower range for their proportion of negative tone. My boss took a look at the data and made up an answer based on a crude assessment of the data and her intuition. But I really wanted something... a little more robust that I could explain to the client.

Btw the way I asked most of my colleagues and none of them know much about stats (to my amazement). They know how to use the tools but no-one seemed to have much understanding of the deeper workings.

I guess I was always good at math and work keeps me from forgetting it all :)
But these are commonly used for any market research I think.

I'm no expert for sure - just have some practical experience.

What draugnar is suggesting makes perfect sense - sometimes it's hard to know what type of analysis/ratios/etc. will give you valuable additional info - so having a template to try out different approaches helps a lot.

@Spyman - one of my first jobs was working on a package called SPC Timesaver by Zontec. I wrote the SPC charting system they used at the time. I also developed sfotware to run various simulations and equations like Guassian predictions of worst case wind event analysis at Fernald (a superfund site). But most of my work has been in the collecting of data points using various digital micrometers at Zontec and, when I was at Hilltop Research, various medical data collection devices that could determine pigmentation, moisturization, flexibility, etc.

I also have been QIFd (Quality Improvement Fundamentals) and trained in Lean Manufacturing (had more than my share of Kaizens) and I just recently completed Six Sigma training. I am working on my Six Sigma Green Belt project right now.

So, I've worked on it from the programming side and from the end-user side.

grrrr... Gaussian