Mean
The mean is the average of repeated measurements, found by adding the trial values and dividing by the number of trials.
Formula
\bar{x} = \frac{\sum x_i}{n}
Definition
The mean is the average of your trials: add up all the measurements and divide by how many there were, written $\bar{x} = \frac{\sum x_i}{n}$. In an experiment, the mean at each level of the independent variable is the value that goes in the last column of the data table and on the graph, because it reduces random error compared to any single trial. It is the best estimate of the true value when errors are random and symmetric, and its reliability improves with sample size, since the standard error of the mean scales as $\sigma/\sqrt{n}$. It cannot correct systematic error, it is sensitive to outliers, and it should be reported with a measure of spread and to a precision consistent with the original measurements.
Example
A cart rolled $82\ \text{cm}$, $85\ \text{cm}$, and $84\ \text{cm}$: $82 + 85 + 84 = 251$, and $251 / 3 \approx 83.7\ \text{cm}$. Dissolving times at $30^\circ\text{C}$ of $25\ \text{s}$, $27\ \text{s}$, and $26\ \text{s}$ give $(25 + 27 + 26)/3 = 78/3 = 26\ \text{s}$, reported with its range of $2\ \text{s}$. Five cart speeds of $2.38$, $2.42$, $2.35$, $2.44$, and $2.41\ \text{m/s}$ sum to $12.00$, so $\bar{x} = 2.40\ \text{m/s}$; with a standard deviation near $0.035\ \text{m/s}$ the standard error is about $0.035/\sqrt{5} \approx 0.016\ \text{m/s}$, and the result is reported as $2.40 \pm 0.02\ \text{m/s}$.
Key Insight
The mean is the best single number to report from repeated trials, because the small errors in each trial tend to cancel out. It can be pulled a long way by one bad trial, so if a time reads $58\ \text{s}$ because the stopwatch started late, check whether it should be repeated before averaging it in. Averaging more trials tightens the mean around whatever the instrument measures, including its bias: precision improves with $n$, accuracy only improves with calibration.