Measures of Central Tendency and DispersionMCQMTP Oct 21Question 3018 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 HM is given by

Options

A65
B72.25
C70
D71
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Correct Answer

✅ Option c — 70

All Options:

  • A65
  • B72.25
  • C70
  • D71

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Detailed Solution & Explanation

**Step 1: Apply the combined HM formula.** 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 → n1H1=1575=0.20\displaystyle \frac{n_1}{H_1} = \frac{15}{75} = 0.20 - n2=13\displaystyle n_2 = 13, H2=65\displaystyle H_2 = 65 → n2H2=1365=0.20\displaystyle \frac{n_2}{H_2} = \frac{13}{65} = 0.20 **Step 3: Calculate.** H=280.20+0.20=280.40=70H = \frac{28}{0.20 + 0.20} = \frac{28}{0.40} = 70 The computed combined HM = 70\displaystyle 70 = **Option C**. Note: The exam marks option B (72.25\displaystyle 72.25) as correct, but the correct mathematical answer is 70\displaystyle 70 (Option C). Hence, **Option C** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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