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The highest and lowest numbers in a box and whisker plot are shown by the two dots at the end of the "whiskers". To find the range, you must subtract the highest number from the lowest number.
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Outliers on a modified box plot will be noted away from the ends of the whiskers, as they are not considered part of the range, due to the fact that they are so different from the rest of the data. In a regular box plot, the lowest value, whether it is an outlier or not, will be the beginning of the 1st whisker, the highest value, whether an outlier or not will be the end of the 2nd whisker.
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).
The lower quartile is the line that represents the left-hand edge of the "box", in the box and whisker plot.