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Virat
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Asked: 2026-10-03T04:21:51+00:00 In:

Given some data with corresponding weights, how would the weighted average change if all the weights are doubled? If required, experiment with some data. What do you observe? Justify your answer using algebra.

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The weighted average does not change. Doubling every weight scales both the numerator and denominator by 2, which cancel out completely, keeping the overall average strictly identical.

Class 9 Ganita Manjari Part 2 All Chapter Solutions
Class 9 Ganita Manjari Part 2 How Quantities Combine Understanding Data Question Answer

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    1. The weighted average remains completely unchanged. Algebraically, if each weight wᵢ is doubled to 2wᵢ, the new mean is Σ(2wᵢxᵢ)/Σ(2wᵢ). Factoring out the common factor of 2 gives [2Σ(wᵢxᵢ)]/[2Σwᵢ]. The factor 2 cancels from both numerator and denominator, leaving the original weighted mean formula intact. Scaling all weights by any constant preserves relative weights.

       

      For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 10 How Quantities Combine Understanding Data Question Answer (2026-27)

      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-10/

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