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Mathematics — CBSE Class 10 board question

Q1. [1]
If the mean and mode of a data are 12 and 21 respectively, then its median is :
  1. (a) 6
  2. (b) 13.5
  3. (c) 15
  4. (d) 14
Previously asked in CBSE board exam
2026 30/1/1 Q17
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer

(c) 15

Using the empirical relationship: $3 \text{ Median} = \text{Mode} + 2\text{ Mean}$
$= 21 + 2(12) = 21 + 24 = 45$
$\therefore \text{Median} = 45 \div 3 = \mathbf{15}$

Source: Chapter 13, Section 13.4 (Remarks)

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Explanation

The key formula to remember is the empirical relationship: $3 \text{ Median} = \text{Mode} + 2\text{ Mean}$. This is stated in the Remarks of Section 13.4. Substituting directly gives Median = 15. Examiners expect students to recall and apply this formula correctly — no derivation needed for an MCQ.

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