Question

What is the mode of 1,1,1,2,2,2,3,3,3,4,4,4,5,5,5

Answer 1

There are three possibilities:

1.  When all the data elements occur with the same frequency, ie., only once or all of the twice or thrice.,  we say that any data item is a mode.

   so there are five possible values of modes.  1 or 2 or 3 or 4 or 5.
   you could report any...  often  the smallest value may be reported.  It depends.

2. In the same case as above,  we can say,  there there is no mode.

3.  We have an empirical formula by Karl Pearson to use.  This formula is true for a moderately skewed or asymmetrical distribution.  It is true for a symmetrical distribution also.

     Mean = (3+6+9+12+15)/15 = 3
     Median = 3
             Mean - Mode = 3 (Mean - Median)

  From this we can find that  Mode = 3.

   We can also see that  the distribution of data is symmetric around 3.  So in that case,    mean = median = mode.

   Best  value of  mode  = 3.