Why bother to plot your data? A simple shortcut is available that will allow you to do your analysis without the data getting in the way. How do you accomplish this breakthrough? Read on.

This marvelous advance in analysis is known as the “data-free graph.” As usual we begin with a collection of data as in figure 1.

Figure 1: Number of blemishes per roll

Now this is way too much detail. We cannot readily absorb this much information, so we simply extract a few summary statistics from our data. First on this list might be the average or a median. A median value for the number of blemishes per roll is 28.5.

Next we need to characterize how the data are spread out above and below the median, so we find the minimum and maximum values for the data. For the number of blemishes per roll these values are 21 and 38 respectively. To further refine our summary of how the data spread out we also find the quartiles for the data. The quartiles for the number of blemishes per roll are 23 and 35.

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