Central Tendency & DispersionMTP March 21Question 3017 of 473
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If there are two groups with 75\displaystyle 75 and 65\displaystyle 65 as harmonic means and containing 15\displaystyle 15 and 13\displaystyle 13 observations. Then the combined H.M. is given by:

Options

A70
B80
C70.35
D69.48
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Correct Answer

✅ Option a — 70

All Options:

  • A70
  • B80
  • C70.35
  • D69.48

Detailed Solution & Explanation

**Step 1: Recall the formula for combined HM.** Hcombined=n1+n2n1H1+n2H2H_{\text{combined}} = \frac{n_1 + n_2}{\frac{n_1}{H_1} + \frac{n_2}{H_2}} **Step 2: Substitute values.** - n1=15\displaystyle n_1 = 15, H1=75\displaystyle H_1 = 75 → 1575=0.2\displaystyle \frac{15}{75} = 0.2 - n2=13\displaystyle n_2 = 13, H2=65\displaystyle H_2 = 65 → 1365=0.2\displaystyle \frac{13}{65} = 0.2 **Step 3: Calculate.** H=15+130.2+0.2=280.4=70H = \frac{15 + 13}{0.2 + 0.2} = \frac{28}{0.4} = 70 The combined HM = 70\displaystyle 70 = **Option A**. Note: The exam gives option B (80\displaystyle 80) as correct, but the mathematical computation gives 70\displaystyle 70 (Option A). Hence, **Option A** is the correct answer.

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