Step 1: A student measures g with a pendulum: T values 2.01, 2.03, 1.99, 2.02, 2.00 s (L = 1.000 m). Find g ± error. Step 2: Mean T̄ = 10.05/5 = 2.010 s. Step 3: Deviations: 0, +0.02, −0.02, +0.01, −0.01. Σd² = 0 + 0.0004 + 0.0004 + 0.0001 + 0.0001 = 0.0010. Step 4: σ_T = √(0.0010/4) = 0.0158 s; σ_T̄ = 0.0158/√5 = 0.00707 s. Step 5: g = 4π²L/T̄² = 39.478/4.0401 = 9.772 m/s². Fractional error in g = 2σ_T̄/T̄ = 2×0.00707/2.010 = 0.00703. Step 6: σ_g = 9.772 × 0.00703 = 0.0687 ≈ 0.07 m/s². Result: g = 9.77 ± 0.07 m/s² — consistent with 9.81. Five repeats shrank the random error by √5; the mean is the result, never one reading.