An aerosol is never composed of particles of a single, uniform size. It is always a mixture, or a distribution, of different sizes. A size distribution is a way of representing this mix by counting how many particles exist within different size ranges, much like a histogram.

A common and useful statistical model for describing aerosol sizes is the log-normal distribution. It has two key advantages: it is defined only for positive values, which prevents the unrealistic possibility of “negative” particle sizes, and it appears as a straight line on a special type of graph (a log-probability plot). This graphical property is a major advantage for scientists, as it allows them to quickly and visually determine the key parameters of an aerosol sample from their data.

A log-normal distribution is described by two key parameters:

• Median Diameter This parameter represents the “middle” or central size of the distribution. However, how you define “middle” matters significantly.

A key insight is that the **MMD is always larger than the NMD**. This is because a few large, heavy particles can contribute most of the total mass, even if they are few in number.

• Geometric Standard Deviation (σg) This parameter measures the “spread” or width of the size distribution. A small σg indicates that the particles are all very similar in size (a narrow distribution). A large σg indicates that there is a wide variety of sizes present (a broad distribution).

Together, these parameters provide a powerful shorthand for scientists to describe the entire population of particles in an air sample.