Step 1: Understand what is being asked.
We must check whether Assertion (A), that a median of 54 follows from a mode of 50 and a mean of 56, is true, and whether Reason (R) correctly explains it. Let us use a different, equally valid form of the empirical relationship between mean, median and mode.
Step 2: Recall an equivalent form of the empirical relation.
The standard relation is $\text{Mode}=3\,\text{Median}-2\,\text{Mean}$. This can be rearranged into another common form used in some textbooks:
\[ \text{Mean} - \text{Mode} = 3(\text{Mean}-\text{Median}) \]
Step 3: Check Assertion (A) using this form.
Substitute Mean $=56$ and Mode $=50$:
\[ 56 - 50 = 3(56-\text{Median}) \]
\[ 6 = 3(56-\text{Median}) \]
Divide both sides by 3:
\[ 2 = 56 - \text{Median} \]
\[ \text{Median} = 56-2 = 54 \]
This matches the value given in Assertion (A), so Assertion (A) is true.
Step 4: Check Reason (R).
Reason (R) claims $\text{Median}=\frac{1}{3}(\text{Mode}-2\,\text{Mean})$. Rearranging our correct relation $\text{Mode}=3\,\text{Median}-2\,\text{Mean}$ for the median gives:
\[ \text{Median} = \frac{1}{3}(\text{Mode}+2\,\text{Mean}) \]
This has a plus sign, not the minus sign written in Reason (R), so Reason (R) is false.
Final Answer:
Assertion (A) is true and Reason (R) is false, matching option (C).
\[ \boxed{\text{Option (C)}} \]