Intensity distribution curve is most reliable- you dont need material properties to calculate it. DLS is best for monomodal size distribution. For multimodal distribution, the DLS interpretation is rather involved. Then you need to see volume / number distribution. The intensity distribution is converted to volume distribution by applying Mie scattering theories which need Refractive index, absorbance as input. Number distributions are of less reliability as a small error in data acquisition can lead to huge errors. The major problem with DLS is that even in a monomodal nano particle colloid, a single micron sized dust particle (unwanted) will overshadow the scattering of nanoparticles and intensity plot will show only the micron sized particle. For DLS, sample preparation is a very important step. I usually look at the correlogram too for ascertaining the quality of data.
Usually, the intensity based particle size is reported, this also depends on whether your sample is monodisperse or polydisperse. As Lila said, Malvern has a lot of material that could help you.
First check the advises given by the program. If the data quality is enough or somehow poor for an analyze you can't trust to any of these results because the samples are may not be stable for analysis. And if they are stable and the concentration is valid then check for the DPI. If the sample requirements are fit then first look at the intensity if there is no such a huge difference between zeta size then compare it with the number and volume. Because for an idealized sample this parameters expected to be equal to each other (at least near) if there is no such obscure condition its better to give intensity mean. Final notes if the data is bimodal or multi, don't forget to take the ratios into account.
Intensity distribution curve is most reliable- you dont need material properties to calculate it. DLS is best for monomodal size distribution. For multimodal distribution, the DLS interpretation is rather involved. Then you need to see volume / number distribution. The intensity distribution is converted to volume distribution by applying Mie scattering theories which need Refractive index, absorbance as input. Number distributions are of less reliability as a small error in data acquisition can lead to huge errors. The major problem with DLS is that even in a monomodal nano particle colloid, a single micron sized dust particle (unwanted) will overshadow the scattering of nanoparticles and intensity plot will show only the micron sized particle. For DLS, sample preparation is a very important step. I usually look at the correlogram too for ascertaining the quality of data.
As Tamas commented, z-average size distribution obtaining by cumulant analysis is the most common and reliable value, however, in this case, your sample should be monodisperse by intensity weighted measurement. Also, the polydispersity (PdI) value should be less than 0.2 at most if you like to refer your sample has relatively narrow size distribution. The height of peak signal (sensitivity) by intensity, volume, and number weighted average size are proportional to radius to 10^6, 10^3, and 1. This means if your sample have 1 million of 10 nm size particles and 1 of 100 nm size particle, then the intensitiy weight size distribution may show two peaks with almost identical height (theoretically) at each size. This is the reason why you should check the DLS peak by intensity weighted size distribution for make sure the data reliability. As Lila mentioned above, "zetasizer nano" manual is a kind of good textbook(?) for beginner like me. Here is a website of DLS measurement protocol; http://ncl.cancer.gov/working_assay-cascade.asp:
Report Z average size of nanoparticles. Graph obtained in terms of intensity or number is better for presenting your results. PDI values should be less than 0.2 nm.
The intensity weighted distribution involves the least assumptions. Not only do the others require assumptions about the sample, but they also assume that there is only one type of analyte with a single set of properties. For accurate, high-resolution distributions of lipid nanoparticle sizes that do not need any assumptions you need an upstream separation technique such as SEC or FFF. See www.wyatt.com/FFF-MALS.
In addition to the above explanations, you would also consider "quality report" to help interpretation of the size data obtained from a dynamic light scattering measurement. Some equipment like Zetasizer Nano provide the mentioned report:
Three distributions are different because they are different averages. The intensity-averaged value is mostly reported, but remember that the scattering intensity is strongly sensitive to the particle size (I~R^6), so if you see two populations in one measurement, the small size population should dominate the distribution in terms of volume or number. Note that if you want to compare the size obtained from DLS and that from microscope, the number-averaged size is more comparable. If you have only one narrowly distributed population, cumulant analysis should be sufficient. But keep in mind that you need to run the measurements at multiple angles and from the correlation decay function, you can obtain the decay rate gamma. Plot gamma vs q^2, the slope should be diffusion coefficient and from there the particle hydrodynamic size can be calculated. Hope this is helpful.