If the mode of a set of data exceeds its mean by 12, then the mode exceeds its median by:

Question

Question

This question was previously asked in

OSSC CGLRE (Mains) Exam (Mathematics) Official Paper (Held On: 23 July, 2023)

Answer 1

Given:

Mode - Mean = 12

Formula Used:

Mode = 3 × Median - 2 × Mean

Calculation:

Let Mode = M, Mean = μ, and Median = Md.

Given M - μ = 12

From the formula, M = 3 × Md - 2 × μ

Substitute M - μ = 12 into the equation:

⇒ 3 × Md - 2 × μ - μ = 12

⇒ 3 × Md - 3 × μ = 12

⇒ 3 × (Md - μ) = 12

⇒ Md - μ = 12 / 3

⇒ Md - μ = 4

Since M - μ = 12, we have:

⇒ M - μ = 12

⇒ M = 12 + μ

And Md - μ = 4, we have:

⇒ Md = 4 + μ

Therefore, the mode exceeds its median by:

⇒ M - Md = (12 + μ) - (4 + μ)

⇒ M - Md = 12 - 4

⇒ M - Md = 8

The mode exceeds its median by 8.

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