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| body | --uriencoded--\rho=\cfrac%7Bm%7D%7BV%7D=\cfrac%7Bm%7D%7Bl%5e3%7D |
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Part I:
single measurement of a single cube, accuracy of scale is Δm=0.2g, accuracy of length measurement is Δl=0.1mm
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| body | --uriencoded--u_%7B\rhorho%7D=\sqrt%7B\sum\limits_%7Bj=1%7D%5e%7BN%7D\left(\cfrac%7B∂fcfrac%7B\partial f(x_j)%7D%7B∂x_j )%7D a%7Bj%7D)%7D%7B\partial x_%7Bj%7D%7Da_%7Bx_j%7D)%5e2 %7D%7Bj%7D%7D\right)%5e2%7D=\sqrt%7B\left(\cfrac%7B∂\rho%7D%7B∂m)%7D acfrac%7B\partial\rho%7D%7B\partial m%7Da_%7Bm%7D\right)%5e2+\left(\cfrac%7B∂\rho%7D%7B∂l)%7D acfrac%7B\partial\rho%7D%7B\partial l%7Da_%7Bl%7D\right)%5e2 %7D%5e2%7D=\sqrt%7B\left(\cfrac%7B1%7D%7Bl%5e3%7D*\Delta a_m%7Bm%7D\right)%5e2+\left(\cfrac%7B-3m%7D%7Bl%5e4%7D*\Delta a_l%7Bl%7D\right)%5e2%7D=\sqrt%7B\left(\cfrac%7B1%7D%7B0.02m%5e3%7D*0.0002kg\right)%5e2+\left(\cfrac%7B-3*0.2kg%7D%7B0.02m%5e4%7D*0.001m\right)%5e2%7D |
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Part II:
Now a statistical analysis of a set of three cubes' densities is conducted:
| length | mass |
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cube 1 | 21mm | 201g |
cube 2 | 22mm | 204g |
cube 3 | 18mm | 194g |
Average of the length:
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| body | --uriencoded--\bar%7Bx%7D_l=\cfrac%7B1%7D%7BN%7D \sum \limits_%7Bi=1%7D%5e%7BN%7Dx_i=\cfrac%7Bx_1+x_2+x_3+⋯+x_N%7D%7BN%7D=\cfrac%7B21+22+18%7D%7B3%7D=20.3mm |
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| body | --uriencoded--u_%7B\rhorho%7D=\sqrt%7B\sum\limits_%7Bj=1%7D%5e%7BN%7D\left(\cfrac%7B∂fcfrac%7B\partial f(x_j)%7D%7B∂x_j )%7D a%7Bj%7D)%7D%7B\partial x_%7Bj%7D%7Da_%7Bx_j%7D)%5e2 %7D%7Bj%7D%7D\right)%5e2%7D=\sqrt%7B\left(\cfrac%7B∂\rho%7D%7B∂m)%7D acfrac%7B\partial\rho%7D%7B\partial m%7Da_%7Bm%7D\right)%5e2+\left(\cfrac%7B∂\rho%7D%7B∂l)%7D acfrac%7B\partial\rho%7D%7B\partial l%7Da_%7Bl%7D\right)%5e2 %7D%5e2%7D=\sqrt%7B\left(\cfrac%7B1%7D%7Bl%5e3%7D*\Delta a_m%7Bm%7D\right)%5e2+\left(\cfrac%7B-3m%7D%7Bl%5e4%7D*\Delta a_l%7Bl%7D\right)%5e2%7D=\sqrt%7B\left(\cfrac%7B1%7D%7B0.0203m%5e3%7D*0.00513kg\right)%5e2+\left(\cfrac%7B-3*0.1997kg%7D%7B0.0203m%5e4%7D*0.00208m\right)%5e2%7D |
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