# Visualisation of *Multiplicative* Contributions

There are many kinds of charts for visualising how a quantity (e.g. number of students in a class) may be broken up into small sub-categories (number of blue-eyed students, number of brown-eyed students, etc.) that sum to the total. A pie-chart or a bar-chart would both work fine.

However, I have a quantity which is produced by multiplying various contributions:

$$\Gamma =\alpha \times \beta \times \gamma \times \cdots$$

I am trying to find a sensible way of visualising the relative contributions of $$\alpha, \beta,\ldots$$ to $$\Gamma$$. My only thought is to make a pie-chart of the logarithms of each:

$$\log \Gamma = \log \alpha + \log \beta + \log \gamma + \cdots$$

but that feels artificial. Are there any standard chart-types that are used to visualise this kind of information? Thanks.

• How would you represent negative logs on a pie chart? What would be the meaning of representing any logarithm as an angle or wedge area in a pie? Indeed, the underlying difficulty attaches to the basic problem of computing "relative contributions" to a total comprised of a sum of positive and negative numbers: what would you mean by that?
– whuber
Dec 3, 2018 at 22:23
• @whuber That's an excellent point, which I hadn't considered as each variable in my problem is a positive contribution (i.e. $\alpha, \beta > 1$.) Once again, I wonder if there are any clever means of visualising these things.
– tom
Dec 4, 2018 at 21:58
• Histograms, boxplots, stem-and-leaf plots, violin plots, bean plots, rugplots, and kernel density plots--to name just a few--are all standard.
– whuber
Dec 4, 2018 at 22:00