Question

You use a force sensor to measure the weight of an object 10 times, and get the following values: 2.8, 2.6, 2.9, 3.1, 2.4, 2.9, 3.2, 2.5, 2.7, 3.0, where all ten values are in units of N. What is the mean weight of the object, as well as the measurement uncertainty of the weight?

Answer 1

Answer: Mean weight = 2.81 N and Measurement of uncertainty = 0.82 N

Step-by-step explanation:

Mean =
`\frac{\text{Sum of observations}}{\text{number of observations}}`

Mean weight is
`($\mu)=(2.8+2.6+2.9+3.1+2.4+2.9+3.2+2.5+2.7+3.0)/(10)`

`=2.81$`

`$\sum_(i=1)^(10)\left(x_(i)-\mu\right)^(2)=0.61`

`$\sigma=\sqrt{(1)/(N-1) \sum_(i=1)^(10)\left(x_(i)-\mu\right)^(2)}`

`=\sqrt{(1)/(10-1) 0.61}=0.082$`

Measurement of uncertainty will be
`$\sigma=0.082$`

hence, Weight
`$W=2.81 \pm 0.082 N$`