Q1. [1] § 13.3 Mode of Grouped Data § 13.4 Median of Grouped Data § 13.5 Summary
If the mean and the median of a data are 12 and 15 respectively, then its mode is :
- (a) $13 \cdot 5$
- (b) $21$
- (c) $6$
- (d) $14$
Previously asked in CBSE board exam
2023 30/5/1 Q10
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
(b) 21
Using the empirical relation: Mode = 3 Median − 2 Mean = 3(15) − 2(12) = 45 − 24 = 21.
Explanation
The key formula is the empirical relationship: 3 Median = Mode + 2 Mean, given in the Remarks of Section 13.4. Rearranging: Mode = 3 Median − 2 Mean. Always remember this formula for MCQs and short-answer questions.
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