Step 1: A student measures the period of a pendulum 5 times: 2.01, 1.98, 2.03, 2.00, 1.99 s. Find the mean, standard deviation, and standard error. Step 2: Mean: x̄ = (2.01+1.98+2.03+2.00+1.99)/5 = 10.01/5 = 2.002 s. Step 3: Deviations from mean: +0.008, −0.022, +0.028, −0.002, −0.012. Squared: 6.4×10⁻⁵, 4.84×10⁻⁴, 7.84×10⁻⁴, 4×10⁻⁶, 1.44×10⁻⁴. Sum = 1.48×10⁻³. Step 4: Sample variance s² = sum/(N−1) = 1.48×10⁻³/4 = 3.7×10⁻⁴ s²; standard deviation s = √3.7×10⁻⁴ ≈ 0.019 s. Step 5: Standard error of the mean = s/√N = 0.019/√5 ≈ 0.0086 s. Result: T = (2.002 ± 0.009) s. The ±0.009 s is the uncertainty of the mean — it shrinks as 1/√N with more readings.