The answer depends on what the graph is of: the distribution function or the cumulative distribution function.
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A bimodal graph in which the modes are at the extrema.
You cannot because the median of a distribution is not related to its standard deviation.
You can't determine velocity from that graph, because the graph tells you nothing about the direction of the motion. But you can determine the speed. The speed at any moment is the slope of a line that's tangent to the graph at that moment.
A graph is represents a function if for every value x, there is at most one value of y = f(x).
You can determine the median test by arranging the data set in some order, ascending or descending, and picking out the middle data item.