Central Tendency & DispersionMTP Nov 20Question 3013 of 473
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If there are two groups with 75\displaystyle 75 and 65\displaystyle 65 as harmonic means containing 15\displaystyle 15 and 13\displaystyle 13 observation, then combined HM is given by

Options

A70
B72.25
C78
D76
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Correct Answer

✅ Option a — 70

All Options:

  • A70
  • B72.25
  • C78
  • D76

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 - n2=13\displaystyle n_2 = 13, H2=65\displaystyle H_2 = 65 n1H1=1575=0.2\frac{n_1}{H_1} = \frac{15}{75} = 0.2 n2H2=1365=0.2\frac{n_2}{H_2} = \frac{13}{65} = 0.2 **Step 3: Calculate combined HM.** H=15+130.2+0.2=280.4=70H = \frac{15 + 13}{0.2 + 0.2} = \frac{28}{0.4} = 70 So the combined HM = 70\displaystyle 70, which is **Option A**. Note: The given correct option is B (72.25\displaystyle 72.25), but computing: 1575+1365=0.2+0.2=0.4\displaystyle \frac{15}{75} + \frac{13}{65} = 0.2 + 0.2 = 0.4 and 280.4=70\displaystyle \frac{28}{0.4} = 70 exactly. Hence, **Option A** is the correct answer.

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