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Mathematics — CBSE Class 10 board question

Q1. [1]
If the difference of mode and median of a data is 24, then the difference of its median and mean is :
  1. A 12
  2. B 24
  3. C 8
  4. D 36
Previously asked in CBSE board exam
2024 30/4/1 Q7
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer

(A) 12

Using the empirical relation: $3 \text{ Median} = \text{Mode} + 2\text{ Mean}$

Given: Mode − Median = 24, so Mode = Median + 24.

$$3\text{ Median} = (\text{Median} + 24) + 2\text{ Mean}$$
$$\text{Median} - \text{Mean} = 12$$

Explanation

The key formula is the empirical relationship 3 Median = Mode + 2 Mean (from Chapter 13, Remarks). Rearranging gives Mode − Mean = 3(Median − Mean), and Mode − Median = 2(Median − Mean). So Median − Mean = (Mode − Median)/2 = 24/2 = 12. Remember this shortcut for MCQs.

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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.