Two measurements of g: 9.80 ± 0.10 and 9.90 ± 0.20 m/s². What is the weighted mean? (Weights = 1/σ².)

Practice question · Numerical answer

Two measurements of $g$ : $9.80 \pm 0.10$ and $9.90 \pm 0.20$ m/s $^{2}$ . What is the weighted mean? (Weights $= 1/\sigma^{2}$ .)

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9.82 (answers within ±0.01 count)

Why

$w_{1} = 1/0.01 = 100, w_{2} = 1/0.04 = 25$ . Weighted mean = (100 $\times9.80 + 25 \times9.90)/125 = 9.82$ .

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