Question

Assertion (A) : If the Mode and Mean of a data are 12 k and 15 k, then Median of the data is 14 k.
Reason (R) : The relation between the Mean, Mode and Median of a data is : Mean = 3 Median – 2 Mode.

• A. Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
• B. Both, Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

An easy way to remember the empirical formula is the "3-2-1" order of words by length:
\[ \text{Mode (4 letters)} = 3 \text{ Median (6 letters)} - 2 \text{ Mean (4 letters)} \]
This helps prevent swapping terms!

Answer 1

The Correct Option is C

Step 1: Isolate Median from the correct empirical relation.
The correct relation is $\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}$, which rearranges to $\text{Median} = \frac{\text{Mode} + 2\,\text{Mean}}{3}$.
Step 2: Substitute the given values to check the Assertion.
\[ \text{Median} = \frac{12k + 2(15k)}{3} = \frac{42k}{3} = 14k \]
This matches the Assertion, so the Assertion is true.
Step 3: Test the Reason's own formula with the same numbers.
The Reason claims $\text{Mean} = 3\,\text{Median} - 2\,\text{Mode}$. Plugging in gives $3(14k) - 2(12k) = 42k - 24k = 18k$, which does not equal the actual Mean of $15k$, so the Reason's formula is false.
\[ \boxed{\text{A is true, R is false}} \]