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Arithmetic mean
12. Mode vs. median vs. mean for unimodal datasets


Below, there are examples of the different possible relationships between the mode, median, and mean:

MEAN = MEDIAN = MODE – For symmetric histograms with one central peak, all measures are equal (mode: red line, median: orange line, mean: blue line).

MEAN = MEDIAN > MODE – One peak on the left shows the mode (red line), which is smaller than the median (orange line) and the mean (blue line). The right tail is quite short, and it is balanced by the observations on the left; this is shown by the position of the median.

MEAN \leq MEDIAN \leq MODE – The median (orange line) is near the peak because there are the same number of elements in the four leftmost bins (4 times 10, or a total of 40) as there are in the rightmost bin, which has 40 elements. The mean (blue line) is shifted to the left because it takes into account elements' values. The mode (red line) stays in the peak with the most frequent values.

MEAN \geq MEDIAN \geq MODE – The position of the mode is obviously at 0 (red line). Due to the values of the elements and the number of each, both the mean (blue line) and the median (orange line) are shifted to the right.