Question: In a recent experiment, I have found the viscosity of glycerol by measuring the time it took for steel balls of measured density and radius to fall a certain distance in the liquid.

Now, I need to compare this data with a theoretical value given by a certain graph of glycerol viscosity by temperature. I have measured the temperature in the lab and know the average temperature throughout the experiment and its error.

In order to compare the values, I need to know how to properly take data from a given (printed) graph and calculate the error of the value.

I don't really know how to approach it, and it is not something that has been explained previously (nor did I find much data online about lab statistics).

A possible method I thought about is to add the resolution errors of the axes and add the error in measured temperature, but that would give an answer with inconsistent units.

Answer: 
Light, even in quantum mechanical form, travels as a wave. Photons as individual particles only exist at the end of propagation, when that wave interacts. 

That wave always propagates at $c$, the speed of light in a vacuum.

So how does refraction work? As the wave moves through a medium, it intersects with (usually) the electrons, causing them to vibrate. That vibration does not exactly follow the wave: the E field causes a force, which causes an acceleration, which builds to velocity. That motion of charge causes the *reradiation* of another, weaker, delayed wave. The combination of the original wave and the reradiated one results in the overall wave being a bit delayed. The more material traversed, the more it’s delayed. In that sense, it’s showing a slower velocity: the more material it goes through, the longer it takes to get there. 

Note that this is a continuous coherent shaping of a wave. It’s not the scattering of point-like particles like balls in a pachinko machine. This is consistent with what we see: there’s no random scattering of light going through clear optical glass
The other answers explain how light appears to slow *when* it is slowed. But sometimes it isn't, and it was helpful for me to think of the limiting cases for light in water.

Imagine light entering water from a vacuum. Water has a molecular spacing on the order of a nanometer, so from the point of view of a photon with wavelength 1000 nm, the water is a sea of electrons. The photon interacts with the medium as a wave in a dielectric, and the other answers describe how wave-particle duality affects our understanding of the photon's travel.

Now imagine a photon with wavelength 0.01 nm -- an X-ray photon. To this photon, the water is mostly vacuum with some giant H2O particles wiggling around. Since the molecular spacing is much larger than the photon's wavelength, it will interact with the water more as a particle, traveling through the underlying vacuum until it scatters with a single H2O molecule. And we see this in the refractive index of water, which [approaches 1 in the nanometer scale](http://www.philiplaven.com/p20.html) (blue line in plot below).

[![credit: philiplaven](https://i.stack.imgur.com/StP37.png)](https://i.stack.imgur.com/StP37.png)