Solution:

(A) Ogive is used to determine the Median. ✅ True

(B) Given:
\( P(A) = \tfrac{1}{2}, \; P(B) = \tfrac{7}{12}, \; P(\text{not A and not B}) = \tfrac{1}{4} \)

\( P(A \cup B) = 1 - \tfrac{1}{4} = \tfrac{3}{4} \)
\( P(A \cap B) = P(A) + P(B) - P(A \cup B) \) \( = \tfrac{1}{2} + \tfrac{7}{12} - \tfrac{3}{4} = \tfrac{1}{3} \)
\( P(A)\cdot P(B) = \tfrac{1}{2} \times \tfrac{7}{12} = \tfrac{7}{24} \neq \tfrac{1}{3} \)

So, A and B are not independent. ❌ False

(C) Empirical relation: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \] ✅ True

(D) Two–digit even numbers from {1,2,3,4,5}:
- Units digit must be even → {2, 4} → 2 choices.
- Tens digit (if repetition allowed) → 5 choices.
\[ \text{Total} = 5 \times 2 = 10 \] ✅ True (with repetition allowed)

✔ Final Answer: (A), (C), and (D) are correct.