Question

Bag + solid (g)	Bag (g)	Solid (g)	umass (g)
18.44	8.22	10.22	± 0.03
22.18	13.15	9.03
20.03	9.89	10.14
19.75	10.21	9.54

1- Determine the combined uncertainty (u_w) of this total net weight

2- Determine the expanded uncertainty (U) for this total net weight at the 95% confidence level. NOTE: You have weighed all units. This is not an extrapolation

Answer 1

Outline to solve the problem:

The mean or average of measurements,

x̅ = (x₁ + x₂ + x₃ + .......)/n, where x₁, x₂, x₃, ..... are the measured values and n = no. of measurements

The sample standard deviation of the measurements or combined uncertainity,

s or uw = [{(x₁ - x̅)² + (x₂ - x̅)² + (x₃ - x̅)² + ........}/(n-1)]^1/2

At 95% confidence level, the expanded uncertainty (U) = 1.96*s/n^1/2

Now, coming to the problem:

x₁ = 10.22, x₂ = 9.03, x₃ = 10.14 and x₄ = 9.54 and n = 4

Now, you can easily solve the problem.

All the very best !!!!