This chart shows the velocities as a function of angle. The straight line represents the average of all the velocities. As you can see, there's a clear quadratic trend (curved line) that better fits the points. This represents air resistance. Of course, a 3rd degree polynomial would do even better, and a 5th degree even better, but at some point the model gets really complicated, and we're just fitting noise, not physics. Think of it this way: There's a bunch of little things you can do with your bottle rocket to affect its flight that isn't changing the angle. You probably did a lot of these things without noticing. There are also some things, like air resistance, you would want your model to include. You need a statistical tool to measure whether or not what you're fitting is actual physics (air resistance) or just noise (experimental error on your part). That statistical tool is called the chi^2 test, but you probably don't have to worry about it. Instead, use the mean and pretend that the velocity(angle) function is a straight line (even though it obviously isnt).
So why is the function actually quadratic? Well, the time you spend in the air is greater for larger angles. so, there's more time for air to slow the rocket. Since that means that the initial velocity slows due to something other than gravity (a quadratic effect), it makes it seem like there's a slower initial velocity for high theta than there actually is. For some trials you obviously hit an updraft in flight, which kept the rocket up longer (these are outliers and should actually be excluded). To avoid these errors you should run the experiment with the same angle multiple times (>20 for statistical purposes) and average these points together, using the scatter (standard deviation) as an error bar for each angle, use the chi^2 test to correct for the quadratic effect, and then average the points using a weighted average based on the scatter of each point.
