This formula outputs the randomized data from a single-column input range.

=CHOOSECOLS(SORT(HSTACK(DataArray, RANDARRAY(ROWS(DataArray),1)),2,TRUE),1)

From inside out...

1. RANDARRAY creates a 1-column array of random numbers with the same size as the input data.
2. HSTACK creates a 2-column array with the DataArray as column 1 and the random number array as column 2.
3. SORT sorts the 2-column array by the random numbers.
4. CHOOSECOLS outputs the first column.