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CDS 2023 · PYQ · Statistics · medium

The sum of deviations of n numbers from 10 and 20 are a, b respectively. If b/a = −4, then what is the mean of these n numbers?

Answer

The correct answer is C: 12. a = Σxᵢ − 10n, b = Σxᵢ − 20n. b/a = −4 ⟹ Σxᵢ − 20n = −4(Σxᵢ − 10n) ⟹ 5Σxᵢ = 60n ⟹ mean = 12.

  1. A.14
  2. B.16
  3. C.12✓ Correct
  4. D.18

Explanation

a = Σxᵢ − 10n, b = Σxᵢ − 20n. b/a = −4 ⟹ Σxᵢ − 20n = −4(Σxᵢ − 10n) ⟹ 5Σxᵢ = 60n ⟹ mean = 12.
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