In a free$-$fall experiment $($see figure below$),$ a ball is dropped through several trials.

Below is the data set for $N=15$ trials of time of fall.

$0\mathrm{.}35,0\mathrm{.}42,0\mathrm{.}38,0\mathrm{.}36,0\mathrm{.}40,0\mathrm{.}37,0\mathrm{.}41,0\mathrm{.}39,0\mathrm{.}34,0\mathrm{.}43,0\mathrm{.}37,0\mathrm{.}35,0\mathrm{.}39,0\mathrm{.}36,0\mathrm{.}38$

The acceleration due to gravity can be calculated as $g=\frac{2h}{t^2},$ where $h=0\mathrm{.}50m.$

Answer the following strictly in THREE decimal places $($on all calculations$).$

Calculate the value of $g$ for EACH trial. What is the mean of $g?$ Recall that

$\stackrel{}{x}=\frac{1}{N}{\displaystyle \underset{i=1}{\overset{N}{}}}{x}_i\frac{?}{b}$

$ar(g)=$ Blank $1\frac{m}{s^2}$

What is the variance of the measurement of $g?$ Recall that

$4,$ If the true value of $g$ is $9\mathrm{.}807\frac{m}{s^2},$ what is your $\%$ error? Recall that

$96$ error $=\frac{\text{l}\text{r}\text{u}\text{e}\text{v}\text{a}\text{l}\text{u}\text{e}-\text{e}\text{x}\text{p}\text{e}\text{r}\text{i}\text{m}\text{e}\text{n}\text{t}\text{a}\text{l}\text{v}\text{a}\text{l}\text{u}\text{e}\text{l}}{\text{t}\text{r}\text{u}\text{e}\text{v}\text{a}\text{l}\text{u}\text{e}}100$

Hint Use $\frac{?}{\text{b}\text{a}\text{r}}(g)$ in the calculation

$\frac{?}{?}\%$ error $=$ Blank $4\%$