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.

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?

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Yến Oanh 4 years 2021-07-22T05:18:48+00:00 1 Answers 97 views 0

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  1. thienan
    0
    2021-07-22T05:20:02+00:00
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    Answer: Mean weight = 2.81 N and  Measurement of uncertainty = 0.82 N

    Explanation:

    Mean =  \dfrac{\text{Sum of observations}}{\text{number of observations}}

    Mean weight is ($\mu)=\frac{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{\frac{1}{N-1} \sum_{i=1}^{10}\left(x_{i}-\mu\right)^{2}}

    =\sqrt{\frac{1}{10-1} 0.61}=0.082$

    Measurement of uncertainty will be  $\sigma=0.082$  

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

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