If there are two groups with 75 and 65 as harmonic means containing 15 and 13 observation, then combined HM is given by

Option a: 70. Solution: Step 1: Recall the formula for combined HM. Hcombined = n1 + n2/1H1 + n2/H2 Step 2: Substitute values. - n1 = 15 , H1 = 75 - n2 = 13 , H2 = 65 n1/H1 = 15/75 = 0.2 n2/H2 = 13/65 = 0.2 Step 3: Calculate combined HM. H = 15 + 13/0.2 + 0.2 = 28/0.4 = 70 So the combined HM = 70 , which is Option A. Note: The given correct option is B ( 72.25 ), but computing: 15/75 + 13/65 = 0.2 + 0.2 = 0.4 and 28/0.4 = 70 exactly. Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 20Question 3013 of 473

All Questions

If there are two groups with $\displaystyle 75$ and $\displaystyle 65$ as harmonic means containing $\displaystyle 15$ and $\displaystyle 13$ 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.**

H_{\text{combined}} = \frac{n_1 + n_2}{\frac{n_1}{H_1} + \frac{n_2}{H_2}}

**Step 2: Substitute values.** -

\displaystyle n_1 = 15

\displaystyle H_1 = 75

\displaystyle n_2 = 13

\displaystyle H_2 = 65

\frac{n_1}{H_1} = \frac{15}{75} = 0.2

\frac{n_2}{H_2} = \frac{13}{65} = 0.2

**Step 3: Calculate combined HM.**

H = \frac{15 + 13}{0.2 + 0.2} = \frac{28}{0.4} = 70

So the combined HM =

\displaystyle 70

, which is **Option A**. Note: The given correct option is B (

\displaystyle 72.25

), but computing:

\displaystyle \frac{15}{75} + \frac{13}{65} = 0.2 + 0.2 = 0.4

and

\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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If there are two groups with 75\displaystyle 7575 and 65\displaystyle 6565 as harmonic means containing 15\displaystyle 1515 and 13\displaystyle 1313 observation, then combined HM is given by