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 Hi my name is Crystal, My question is under what circumstancs will the mean, the median, and the mode all have the same value?

Hi Crystal. Here are some sets where that is true. See if you can decide how to describe what you see:

a) { 5 }
b) {1, 1, 1, 1, 1}
c) {10, 100, 100, 100, 190}
d) {-2, 0, 0, 2}

Think about eliminating things. The "mode" value must exist in the set. Whatever is left over has to "balance out" in order for the mean to equal the mode. The mode must also be the most common value in the set.

The mode is not the median unless

1. the (number of values below the mode + the number of values larger than the mode) > the number of values below the mode,

2. the (number of values below the mode + the number of values larger than the mode) > the number of values larger than the mode.

I hope these hints are enough to get you started.

Cheers,
Stephen La Rocque and Harley Weston

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.