Central Tendency & DispersionMTP June 24 Series IQuestion 3206 of 473
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Suppose a population A has 100\displaystyle 100 observations 101,102,103,...,200\displaystyle 101, 102, 103, ..., 200 and another population B has 100\displaystyle 100 observations 151,152,153,...,250\displaystyle 151, 152, 153, ..., 250. If VA\displaystyle V_A and VB\displaystyle V_B represents the variance of the two populations respectively, then VA/VB\displaystyle V_A / V_B ______.

Options

A94\displaystyle \frac{9}{4}
B1\displaystyle 1
C49\displaystyle \frac{4}{9}
D23\displaystyle \frac{2}{3}
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Correct Answer

✅ Option b — 1\displaystyle 1

All Options:

  • A94\displaystyle \frac{9}{4}
  • B1\displaystyle 1
  • C49\displaystyle \frac{4}{9}
  • D23\displaystyle \frac{2}{3}

Detailed Solution & Explanation

**Key Observation:** - Population A: 101, 102, ..., 200 — These are 100 consecutive integers. - Population B: 151, 152, ..., 250 — These are also 100 consecutive integers. Population B is obtained by adding 50 to each element of Population A: bi=ai+50b_i = a_i + 50 **Effect on Variance:** Adding a constant to every observation does NOT change the variance. Variance is independent of change of origin. VA=VBV_A = V_B **Therefore:** VAVB=1\frac{V_A}{V_B} = 1 Hence, **Option B** is the correct answer.

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