Find median given large amount of data

Question

Listing all the possibilities would take time. Would there be a faster and more efficent way to find the median?

Answer 1

The median of a data set is the "middle" point. Let's do this by area of the "bars" on the graph. The first bar has an area of 40. The second of 50, third of 40, fourth of 30 and last of 10. If we "shade" the first bar, we must shade a total area of 40 on the right. So the 28 and 29 bars have a combined area of 40 and therefore we shade them. Now we shade the smaller of the two remaining, which is the 27 bar of area 40. Now we shade the bottom area of the 26 bar and see that we still have an area of 10 in that bar and nothing else to cancel with. Therefore, the only possibility for the median is 26.

This is basically the same as listing them all out, except we are canceling groups of them at a time, rather than individually.