In a hypothetical scenario, the National Institute of Standards and Technology has received a new replica of The Kilogram. It is weighed five times. The measurements are as follows, in units of micro-grams above 1 kg: 114.3, 82.6, 136.4, 126.8, 100.7.a) Is it possible to estimate the uncertainty in these measurements? If so, estimate it. If not, explain why not.b) Is it possible to estimate the bias in these measurements? If so, estimate it. If not, explain why not.

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a) Given datax={114⋅3,82⋅6,136⋅4,126⋅8,100⋅7}Mean x―=ξxn=114⋅3,82⋅6,136⋅4,126⋅8,100⋅75=560⋅85x―=112⋅16 mgSo σ=1n−1(ξx2−nx―2)→ |1|ξx2=(114⋅3)2+(82⋅6)2+(136⋅4)2+(126⋅8)2+(100⋅7)2=64710.94Substitute ξx2  x― valies in |1|=15−1(64710.94−5(112⋅16)2)=14(1811⋅612)=452⋅903σ=21⋅28 mgb) Since we dont know the true Value Is it Not possible to estimate the bias in these measurements.

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