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Question:

A medical student is conducting a chart review of patients admitted to the local emergency department with acute pancreatitis.  He is interested in comparing blood glucose levels between mild and severe cases.  Before attempting to compare the mean blood glucose levels between the 2 groups of patients, he decides to conduct a descriptive analysis of the variables in each group.  Blood glucose levels in patients with severe acute pancreatitis were found to have a strong positively skewed distribution.  Which of the following is most likely to be true regarding the data for the severe acute pancreatitis group?

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Explanation:

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The symmetrical bell-shaped curve is usually cited as the prototypical curve describing the distribution of a continuous variable.  However, in actual research scenarios, continuous variables often have asymmetrical distributions.  When a distribution curve is asymmetric, it is either positively or negatively skewed:

  • In a positively skewed distribution, there is an increased number of observations with larger-than-expected magnitudes (ie, extreme values) that shift the mean toward the right, producing a longer slope of the curve ("tail") on the positive side of the distribution.
  • In a negatively skewed distribution, there is an increased number of observations with smaller-than-expected magnitudes that shift the mean toward the left, producing a longer slope of the curve ("tail") on the negative side of the distribution.

In general, in a positively skewed distribution, the mean is the most shifted in the positive direction, followed by the median and then the mode (mode < median < mean).  In such a situation, the median often reflects a central tendency better than the mean does.

(Choices A and B)  In perfectly normal distribution curves where there is no skew, all 3 measures of central tendency are precisely equal: mean = median = mode.  If a minor skew is present, the 3 measures are approximately equal.

(Choices D and E)  In general, in a negatively skewed distribution (with the "tail" on the left), the mean is the most shifted in the negative direction, followed by the median and then the mode.

Educational objective:
In general, in a positively skewed distribution, the mean is the most shifted in the positive direction (to the right), followed by the median and then the mode.  In such a situation, the median often reflects a central tendency better than the mean does.