Mean, Median & Mode

The USMLE tests your understanding of where the mean, median & mode are located, relative to each other, in an asymmetrical data set (or, on an asymmetrical curve known as skewed curve).  The good news is that solving these problems is a LOT easier than writing the previous sentence because I can’t give away all my secrets on-line!

Core concepts of Mean, Median & Mode

The mean, median and mode are tools statisticians use to say, “this is the middle-point of your data.”  Math books call it (essentially), “central tendency.”  The mean has become synonymous with word, “average” but all three are a type of “average.”  Researchers will select either the mean, median or mode depending on the type of data they are working with such as heavily skewed data or, if researchers need to identify the most commonly occurring datum.
Mean:    sum of all values ÷ n
Median: middle number
Mode:    most frequent number

Solving / answering high yield Mean, Median & Mode questions

Let's use a sample data set of observations:  1, 3, 2, 3
Mean:   (1+3+2+1)/4 = 9/4 = 2.25
Median: (1, 2, 3, 3) = (2+3)/2 = 2.50 (re-write data set in numeric order!!)
Mode:   (1, 3, 2, 3) = 3.00


That's the mean, median and mode, for the USMLE and similar exams, in a nutshell!! But the USMLE biostat workbook does much more.  One trick I present simplifies these concepts 1, 2, 3 – if you can write 1, 2, 3 then you can solve any mean, median, mode, and skewed curve problem (I show how intuitively skewed curves are tied to the mean, median and mode).  

The USMLE biostat workbook provides more details, more tricks and commonly-presented word problems with thorough explanations. It also presents a handful of exotic problems: weighted average (seen in the USMLE), and several ways the USMLE can ask trick questions. Buy now!

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