Measures of Central Tendency and DispersionPYQ Sept 25Question 4471 of 473

If there are two groups with 10 and 12 observations and harmonic mean of the two groups are 3 and 5 respectively, then the combined Harmonic mean is

Options

A8.0

B2.0

C3.8

D4.0

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Correct Answer

✅ Option c — 3.8

All Options:

A8.0
B2.0
C3.8
D4.0

Detailed Solution & Explanation

Let us compute the combined Harmonic Mean (

\displaystyle H

) of two groups:
1. **Given Data**:
- Number of observations in Group 1:

\displaystyle n_1 = 10

- Harmonic Mean of Group 1:

\displaystyle H_1 = 3

- Number of observations in Group 2:

\displaystyle n_2 = 12

- Harmonic Mean of Group 2:

\displaystyle H_2 = 5

2. **Formula for Combined Harmonic Mean**:

H = \frac{n_1 + n_2}{\frac{n_1}{H_1} + \frac{n_2}{H_2}}

3. **Calculation**:
Substitute the given values into the formula:

H = \frac{10 + 12}{\frac{10}{3} + \frac{12}{5}}

H = \frac{22}{\frac{10 \times 5 + 12 \times 3}{15}}

H = \frac{22}{\frac{50 + 36}{15}}

H = \frac{22}{\frac{86}{15}}

H = \frac{22 \times 15}{86} = \frac{330}{86}

H = \frac{165}{43} \approx 3.837

Rounding to one decimal place gives

\displaystyle 3.8

.
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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