Question

exercise 6: a student measure the mass of a marble with different devices and methods

device 1	device 2	device 3	device 4	device 5

a) do you trust all the measurements? is there any outlier? what should we do with it?
b) what is the most precise measurement?
c) what is the most accurate measurement?
b) find the average:
c) find the random error:
d) write the value with its uncertainty and units:
e)find the percentage of uncertainty

Explanation:

Step1: Identify outlier

11g is far from others, so it's an outlier and we should discard it.

Step2: Find most precise

Device 1 measures to two - decimal places (5.02g), so it's most precise.

Step3: Calculate average (excluding outlier)

$\frac{5.02 + 4.9+5.0 + 4.8}{4}=\frac{19.72}{4}=4.93$g

Step4: Estimate random error

Without more data, assume standard deviation of remaining values as random error. First, find mean - square deviation: $\frac{(5.02 - 4.93)^2+(4.9 - 4.93)^2+(5.0 - 4.93)^2+(4.8 - 4.93)^2}{4 - 1}\approx0.011$. Random error $\approx\sqrt{0.011}\approx0.1$g

Step5: Find percentage of uncertainty

$\frac{0.1}{4.93}\times100\%\approx2\%$

Answer:

a) No, 11g is outlier, discard it.
b) 5.02g (Device 1).
c) 4.93g.
d) $4.93\pm0.1$g.
e) 2%.