The experimental data's low standard deviation value paired with the 20.0% error calculation when compared to the theoretical result shows that there's a factor in the projectile launcher that consistently limits its experimental performance.
A possible explanation for part of this difference could be the ball place-holder (contact lens package) that was used. While this place-holder doesn't exert an obvious negative force on the projectile, like the nails used in the initial design, a negative frictional force between the surface of the projectile and contact lens package could contribute to a smaller actual value than the experimental value that negates any form of resistant force.
A more likely reason for this 20.0% error though is the point of release of the projectile. If the ball was released at a point before reaching 20 degrees, then its distance traveled would have decreased. This is not due to the greater angle of projection, since this angle doesn't effect horizontal displacement, but less kinetic energy achieved at the point of release. The estimate of distance traveled was calculated with the presumption that the elastic would entirely return to equilibrium. If the projectile was released before this point, then kinetic energy would be less because there is still some potential elastic energy left in the elastic that has yet to be converted. Consequently, the displacement of the elastic is also less. A reason for an early release of the projectile could simply be gravity, since an angle of 20 degrees to the vertical is quite steep and it is very possible that the projectile could've left its place-holder on the rotating piece at an earlier incline/position.
Eliminating the difference between theoretical and experimental results could be by basing your calculations and device around an angle of projection of less vertical incline. For example, instead of making the point of release 20 degrees to the vertical, which could be unrealistic, an equilibrium that lies at an angle of 45 degrees may be better. In order to make up or the decrease in displacement of the elastic, there are several factors that could be taken into consideration. These may also increase the overall effectiveness of the projectile launcher and make the projectile go further.
Using a material with a larger spring constant will prove very effective since the elastics used were of ordinary household material. Even incorporating a spring that is not too rigid may prove drastically different in result. Also, using a longer rotating arm-piece will increase the displacement of the elastic, creating a larger build-up in elastic potential energy. Developing a way to attach the elastics to the rotating piece at a more parallel placement will also have some help on a longer horizontal displacement. The inward slant (in this case, 10 degrees and 34 degrees) takes away from the elastic potential energy collected since a resultant value must be considered.
