nagasenaz

2020-11-20

The weight of an object is given as $67.2±0.3g$. True or false:
a) The weight was measured to be 67.2 g.
b) The true weight of the object is 67.2 g.
c) The bias in the measurement is 0.3 g.
d) The uncertainty in the measurement is 0.3 g.

Delorenzoz

Step 1
a.
The form of the measurements of weight of an object is $67.2±0.3g$.
Justification:
The format of a process' measurements is,
Measured value $\left(\mu \right)±$ Standard deviation $\left(\sigma \right)$
Here, the population standard deviation will be sample standard deviation and the measured value will be sample mean for a random sample.
The form of the measurements of weight of an object is $\left(67.2±0.3g\right)$.
Here, the measured value or mean of the weight of an object is $67.2g$.
Thus, the measured value of weight is $67.2g$.
Therefore, the given statement “The weight was measured to be $67.2g$” is true.
b.
The form of the measurements of weight of an object is $67.2±0.3g$ does not indicate the true value of weight of an object.
Therefore, the given statement “The true weight of an object is $67.2g$” is false.
Step 2
c.
Bias:
Error in the measured value is the distinction between a measured value and its true value. A measurement error can happen in one of two ways. They are:
Systematic error or bias.
Random error.
The systematic error or bias is same for all the measurements whereas the random error varies from measurement to measurement.
The general formula to obtain bias is,
bias=mean measurement−true value.
The form of the measurements of weight of an object is $67.±0.3g$.
Here, the measured value or mean of the weight of an object is 67.2g.
Here, the true value of weight is unknown.
In order to estimate the bias, the additional information about the true value is mandatory. Thus it is not possible to estimate of the bias in the measurements of weight without the true value of weight of an object.
Here, 0.3 does not indicate bias in the measurements.
Thus, the given statement “The bias in the measurement is $0.3g$” is false.
d.
Uncertainty:
The uncertainty of a process is determined by the standard deviation of the measurements. In other words, it can be said that, measure of variability of a process is known as uncertainty of the process.
Hence, it can be said that uncertainty is simply $\left(\sigma \right)$.
Standard deviation or uncertainty of first thermometer:
The form of the measurements of weight of an object is $67.±0.3g$.
Here, the standard deviation of weight of an object is $0.3$.
Hence, the given statement “The uncertainty in the measurement is $0.3g$” is true.

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