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

Select Your Answer (Keyboard: A, B, C, D)
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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_{combined\displaystyle \text{combined}} = n1+n2n1H1+n2H2\displaystyle \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=0.2n1H1=1575=0\displaystyle \frac{n_1}{H_1} = \frac{15}{75} = 0.2 n2H2=1365=0.2n2H2=1365=0\displaystyle \frac{n_2}{H_2} = \frac{13}{65} = 0.2 **Step 3: Calculate combined HM.** H=15+130.2+0.2=280.4=70H = \displaystyle \frac{15 + 13}{0.2 + 0.2} = \frac{28}{0.4} = 70 So the combined HM = $70$, which is **Option A**. Note: The given correct option is B ($72.25$), but computing: $1575+1365=0\displaystyle \frac{15}{75} + \frac{13}{65} = 0.2 + 0.2 = 0.4and\displaystyle and280.4=70\displaystyle \frac{28}{0.4} = 70$ exactly. Hence, **Option A** 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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