Example Problem: You and some classmates are testing some “identical” model rocket engines. 
One team makes measurements of the duration “t” of burn for several rocket engines. 
Another team makes measurements of the acceleration “a” created by several rocket engines during some practice launches.
You want to calculate the expected distance “y” (i.e., height) reached by these rockets, along with appropriate statistics about this computed result.
Use Mathematica to compute y, (Subscript[σ, y]),(Subscript[σ, my]), and (Subscript[r, y]) using this data. 
Check: final answers should be: y = 732.488 m, (Subscript[σ, y]) = 170.120 m,(Subscript[σ, my]) = 35.953 m, and (Subscript[r, y]) = 114.746 m.

ClearAll["Global`*"]
t={5.19,5.12,6.64,5.92,6.08,6.68,5.99,5.31,6.16,4.54,6.29,6.22,5.81, 4.40,5.85,5.58,4.56,6.25,5.82,5.16,5.60,6.12,5.84}; (* in seconds *)
a={45.67,43.26,41.93,49.39,47.01,46.82,45.26,46.27,40.82,43.06,44.02,52.49,41.14,44.35,44.34,44.88,45.47}; (* in m/(s^2) *)
(* the following lines are all just placeholders waiting for you to enter a "real" equation! *)
(Subscript[L, t]) = 0; (* i.e., how many "t" measurements are there? *)
(Subscript[L, a])=0;
(Subscript[t, ave]) = 0;
(Subscript[a, ave])=0;
(Subscript[σ, t]) = 0;
(Subscript[σ, a]) = 0;
(Subscript[σ, mt])=0;
(Subscript[σ, ma])=0;
(Subscript[r, t])=0;
(Subscript[r, a])=0;
y=0;
(Subscript[σ, y]) = 0; (* best to do derivatives by hand! *)
(Subscript[σ, my]) = 0;(* best to do derivatives by hand! *)
(Subscript[r, y]) = 0;(* best to do derivatives by hand! *)
Print["There were ",(Subscript[L, t])," measurements of time, and ",(Subscript[L, a])," measurements of acceleration."]
Print["The time measurements resulted in ",(Subscript[t, ave])," ± ",(Subscript[σ, mt])," s."]
Print["The acceleration measurements resulted in ",(Subscript[a, ave])," ± ",(Subscript[σ, ma])," m/(s^2)."]
Print["The height computations resulted in ",(Subscript[y, ave])," ± ",(Subscript[σ, my])," m."]
Print["The height also had σ = ",(Subscript[σ, y])," and r = ",(Subscript[r, y])," m."]