A train's speed in m/s was measured at the times 0, 2, 5, 9, 10 and 12 s: 0, 6, 10, 10, 4 and 0…

Check. The trapezoids are: $\tfrac{1}{2}(0 + 6) \times 2 = 6$, then $\tfrac{1}{2}(6 + 10) \times 3 = 24$, then $\tfrac{1}{2}(10 + 10) \times 4 = 40$, then $\tfrac{1}{2}(10 + 4) \times 1 = 7$, then $\tfrac{1}{2}(4 + 0) \times 2 = 4$. The sum is 81. The first two are 30. The mean speed is $81 / 12 = 6.75$ m/s.