Yes. For example, in the sequence {1,2,2,2,2,3,4,7} 2 is the median, and 2 is also the mode.
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In a normal distribution the mean, median and mode are all the same value.
For the set 3 4 5 8 5, the mean median and mode all have the same value.
All three increase by that same value.
Mean, median, and mode are all equal in a normal distribution.
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