What the task is actually asking for is the 5 numbers used to draw a boxplot. This has nothing to do with "big data", or with producing a "smaller array". Requiring that the five numbers yield the same boxplot if they are treated as data is pretty useless: the task emphasizes space reduction, but it will not save space.
There are several conventions for boxplot statistics. Not all statistical programs draw boxplots like R.
Also, 5 numbers are obviously not enough to reproduce a boxplot, as outliers are usually drawn as well. This is not a problem if we admit we don't need the outliers.