IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 12

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Statistics, with the answer and a step-by-step solution.

StatisticsModern MathematicsMultiple choiceMedium
Five observations {x}_{1},{x}_{2}, ...,{x}_{5} are transformed using {y}_{i}= 2{x}_{i}- 3. If \sum_{i=1}^{5}{{y}_{i}}= 35 and \sum_{i=1}^{5}{{y}_{i}^{2}}= 325, what is \sum_{i=1}^{5}{{x}_{i}^{2}}?
  1. A
    145
  2. B
    185
  3. C
    165
  4. D
    125
Pick an option, then check.
Answer & solution

Answer: Option A

From yᵢ = 2xᵢ − 3, summing over the five values gives Σyᵢ = 2Σxᵢ − 15.

So 35 = 2Σxᵢ − 15, which gives Σxᵢ = 25.

Squaring the transformation: yᵢ² = 4xᵢ² − 12xᵢ + 9.

Summing: Σyᵢ² = 4Σxᵢ² − 12Σxᵢ + 45.

Substituting the known values: 325 = 4Σxᵢ² − 12(25) + 45.

325 = 4Σxᵢ² − 300 + 45, so 4Σxᵢ² = 580.

Σxᵢ² = 145.

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