Establish the relationship

The empirical relation between mean, median, and mode is given by $\text{Mode} = 3Median - 2Mean$.

$\text{Mode} = 3Median - 2Mean$

Rearrange the formula

To express the difference $(\text{Mode} - \text{Median})$, we rewrite the formula: $\text{Mode} - \text{Median} = 3Median - 2Mean - \text{Median} = 2Median - 2Mean = 2(\text{Median} - \text{Mean})$. Alternatively, subtract $\text{Mean}$ from both sides: $\text{Mode} - \text{Mean} = 3Median - 3Mean = 3(\text{Median} - \text{Mean})$.

$\text{Mode} - \text{Mean} = 3(\text{Median} - \text{Mean})$

Solve for the difference

Given $\text{Mode} - \text{Mean} = 16.2$, we find the difference between median and mean: $16.2 = 3(\text{Median} - \text{Mean})$, so $\text{Median} - \text{Mean} = 5.4$. Now, we need the difference $\text{Mode} - \text{Median}$. Using $\text{Mode} - \text{Median} = 2(\text{Median} - \text{Mean})$, we get $2 \times 5.4 = 10.8$.

$\text{Mode} - \text{Median} = 10.8$