Question

Four different people measure the time needed for a rock to hit the floor when dropped:

t1 = 3.3 s
t2 = 3.4 s
t3 = 3.1 s
t4 = 2.9s

a. Find the mean value of the experiment, in sec.
b. Find the standard deviation, in s. 0.122.
c. Find the standard error, in s. 0.061.

Answer 1

Answer:

3.175 s

0.221735578261 s

0.11086778913 s

Explanation:

Mean is given by

$t=\dfrac{3.3+3.4+3.1+2.9}{4}\\\Rightarrow t=3.175\ s$

The mean is 3.175 s

Standard deviation is given by

$s=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\bar{x})^2}$

$s=\sqrt{\dfrac{(3.3-3.175)^2+(3.4-3.175)^2+(3.1-3.175)^2+(2.9-3.175)^2}{4-1}}\\\Rightarrow s=0.221735578261\ s$

The standard deviation is 0.221735578261 s

Standard error is given by

$\sigma_x=\dfrac{s}{\sqrt{N}}\\\Rightarrow \sigma_x=\dfrac{0.221735578261}{\sqrt{4}}\\\Rightarrow \sigma_x=0.11086778913\ s$

The standard error is 0.11086778913 s

Checked in excel