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If the data are quantitative they must have a median. If there is no median it is only because the data are qualitative and, in that case, a box and whiskers plot is meaningless.
Both plots are ways of visualizing data. Both are used in statistical analyses. But I would say they are not very alike. Histograms show the relative or absolute frequency of data in specified (usually equal) intervals. The range of values in a single data set can be seen on a histogram. A box shows how the median and range of various datasets vary over time (or some other variable).
Parallel box and whisker plots are regular box and whisker plots, but drawn "one-above-the other" on the piece of paper. To enable to do this easily, draw an x-axis which is big enough for the largest value in the data, and small enough for the smallest value in the data (in the entire collection of data). Plot each box-and-whisker diagram below each other.
A histogram can handle data when the bars are not all of the same width. This is particularly important for data which are skewed.
The [vertical] sides of the box go from the Lower Quartile to the Upper Quartile. The Median is drawn parallel to these sides. The whiskers stretch out from half-way up the sides of the box to the minimum and the maximum.