Central Tendency & DispersionPYQ June 24Question 2877 of 473
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If there are two groups containing 40 and 30 observations and have arithmetic means as 50 and 60, then the combined arithmetic mean is

Options

A55.48
B56.35
C54.28
D50.28
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Correct Answer

✅ Option c — 54.28

All Options:

  • A55.48
  • B56.35
  • C54.28
  • D50.28

Detailed Solution & Explanation

**Step 1: State the formula for combined mean.** xˉ12=n1xˉ1+n2xˉ2n1+n2\bar{x}_{12} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2} **Step 2: Substitute values.** n1=40\displaystyle n_1 = 40, xˉ1=50\displaystyle \bar{x}_1 = 50, n2=30\displaystyle n_2 = 30, xˉ2=60\displaystyle \bar{x}_2 = 60. xˉ12=40×50+30×6040+30=2000+180070=380070=54.2857...≈54.28\bar{x}_{12} = \frac{40 \times 50 + 30 \times 60}{40 + 30} = \frac{2000 + 1800}{70} = \frac{3800}{70} = 54.2857... \approx 54.28 Hence, **Option C** is the correct answer.

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