Question

**Assertion (A):** If values of Mode and Mean of a data are 60 and 66 respectively, then the value of Median is 64. **Reason (R):** For any data, $2	ext{ Mean} = 	ext{Mode} + 3	ext{ Median}$.

Accepted Answer

C. The empirical formula is $	ext{Mode} = 3	ext{ Median} - 2	ext{ Mean}$. For Mode = 60, Mean = 66: $60 = 3	ext{ Median} - 2(66) \implies 3	ext{ Median} = 192 \implies 	ext{Median} = 64$. Thus Assertion (A) is true. Reason (R) states $2	ext{ Mean} = 	ext{Mode} + 3	ext{ Median}$, which is incorrect (it should be $3	ext{ Median} = 	ext{Mode} + 2	ext{ Mean}$). Thus Reason (R) is false.

Empirical relationship between mean, median and mode

Explanation

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