Bar Graphs of Population Distributions
We start with Figure 1, the bar graph of the hospital length of stay for all patients with diabetes. In the National Inpatient Sample, that includes just over 1 million patient stays. Note that the distribution has a very heavy tail with the maximum stay of about 354 days. The average length of stay is equal to 5 days with a standard deviation of 5.8 days. Figure 2 reduces the values on the x-axis to a maximum of 50 days so that we can focus on this part of the graph.
Figure 1. Length of hospital stay for patients with diabetes
Figure 2. Length of stay limited to 50 days maximum
In Figure 2, note the gaps that occur because of rounding in the length of stay. It suggests that the information is not completely accurate because of this rounding.
Figure 3 gives the best normal estimate of the population distribution. It significantly under-values the probability at the low end, but also does not adequately estimate the outliers, or extreme patient outcomes.
Figure 3. Normal estimate of population distribution
Figure 4 gives an exponential distribution estimate. It better follows the pattern of the bar graph, but it still under-values the height of the bars.
Figure 4. Exponential estimate of population distribution