Question

You attempt to determine the validity of a bathroom scale by repeatedly placing 20 lb of accurate weights on it.
Ten readings were obtained with values of:
20.2, 20.2, 20.6, 20.0, 20.4, 20.2, 20.0, 20.6, 20.0, and 20.2 lb.

Estimate the systematic error and the maximum random error of the measurements.

Answer 1

Answer:

Systematic error = 0.4 lb

Maximum random error = 0.36 lb                    

Step-by-step explanation:

We are given the following data set in lb:

20.2, 20.2, 20.6, 20.0, 20.4, 20.2, 20.0, 20.6, 20.0, 20.2

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{202.4}{10} = 20.24$

Systematic error:

It is defined as the difference between the average value of readings and the true value.

$\text{Systematic error} = 20.24 - 20 = 0.24\text{ lb}$

Maximum random error:

It is the maximum absolute value of difference between reading minus the average of readings.

Differences: -0.04, -0.04, 0.36, -0.24, 0.16, -0.04, -0.24, 0.36, -0.24, -0.04

Absolute value of difference: 0.04, 0.04, 0.36, 0.24, 0.16, 0.04, 0.24, 0.36, 0.24, 0.04

Maximum random error = 0.36 lb