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Mathematics — CBSE Class 10 board question

Q1. [1]
The median and mode of a distribution are 25·2 and 26·1 respectively. The mean of the distribution is :
  1. A 24·75
  2. B 24·25
  3. C 24·3
  4. D 25·5
Previously asked in CBSE board exam
2026 30/3/1 Q16
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer

Using the empirical relationship: 3 Median = Mode + 2 Mean

3(25.2) = 26.1 + 2 Mean → 75.6 – 26.1 = 2 Mean → Mean = 49.5/2 = 24.75

Answer: (A) 24·75

Explanation

The key formula is the empirical relation: 3 Median = Mode + 2 Mean (stated in Chapter 13, Remarks section). Rearranging gives Mean = (3 Median – Mode) / 2. Substitute Median = 25.2, Mode = 26.1 to get (75.6 – 26.1)/2 = 24.75. Examiners expect you to recall and apply this formula directly.

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Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.