Question

exercise 5: several students measure the time it takes for a tennis ball to fall from 1m.

student 1 measurement	student 2 measurement	student 3 measurement	student 4 measurement	student 5 measurement

a) do you trust all the measurements? is there any outlier? what should we do with it?
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

0.89s is far from others, so it's an outlier and we may discard it.

Step2: Calculate average

$\bar{t}=\frac{0.55 + 0.43+0.58 + 0.49}{4}=0.5125s$

Step3: Calculate random error

Assume each measurement has equal - weight, without more info, we can use the range of non - outlier data. Error $=\frac{0.58 - 0.43}{2}=0.075s$

Step4: Write value with uncertainty

$0.51\pm0.08s$

Step5: Calculate percentage of uncertainty

$\text{Percentage of uncertainty}=\frac{0.08}{0.51}\times100\%\approx16\%$

Answer:

a) No, 0.89s is an outlier and can be discarded.
b) 0.5125s
c) 0.075s
d) $0.51\pm0.08s$
e) 16%