The Five-Number Summary uses intervals to describe the variation in different segments of your data. The longer the interval, the greater the variation. Some people will misinterpret a box plot. For example, given a box plot with the Q3-Max whisker considerably longer than the Min-Q1 whisker, one could think, "Wow, there are a lot more data in the highest interval than there are in the lowest interval." We're used to associating length with "how many" rather than "how far apart," and we forget that the same number of values falls within each of these intervals.
It is also important to note the difference between a histogram and a box plot, another potential source of confusion. To construct a histogram, you prescribe intervals of uniform length and then count how many data values fall within each interval. To determine the five numbers for the box plot, you do the reverse: prescribe how many data values you want in each interval and then determine the intervals.
Fathom Software, used by the onscreen participants, is helpful in creating graphical representations of data. You can use Fathom Software to complete Problems D2-D3. For more information, go to the Key Curriculum Press Web Site at
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