To find the percentile of the value 84, we first need to find the total number of values in the data set. In this case, there are 6 values in total.
Now, let's arrange the values in ascending order:
23, 28, 51, 52, 68, 84
Next, we need to find the rank of the value 84 in the ordered list:
Since 84 is the 6th value and there are a total of 6 values, the rank of 84 is 6.
The next step is to calculate the percentile using the formula:
\text{Percentile} = \left( \frac{{\text{Rank} - 0.5}}{{\text{Total number of values}}} \right) \times 100
Substitute the values into the formula:
\text{Percentile} = \left( \frac{{6 - 0.5}}{6} \right) \times 100 = \left( \frac{5.5}{6} \right) \times 100 = 0.9167 \times 100 = 91.67\%
Rounded to the nearest whole percentile, the value 84 is the 92nd percentile.
Therefore, 84 represents the 92nd percentile.
\boxed{92}