The harmonic mean A and B is 1/3 and harmonic mean of C and D is 1/5 . The harmonic mean of ABCD is

Option b: 1/4. Solution: Step 1: Recall the formula for Harmonic Mean of two numbers. HM(A, B) = 2/1A + 1/B = 1/3 So 1/A + 1/B = 6 . HM(C, D) = 2/1C + 1/D = 1/5 So 1/C + 1/D = 10 . Step 2: Compute HM of all four values A, B, C, D. HM(A,B,C,D) = 4/1A + 1/B + 1/C + 1/D = 4/6 + 10 = 4/16 = 1/4 Hence, Option B is the correct answer.

The harmonic mean $A$ and $B$ is $1/3$ and harmonic mean of $C$ and $D$ is $1/5$. The harmonic mean of $ABCD$ is

The correct answer is Option b: $1/4$. **Step 1: Recall the formula for Harmonic Mean of two numbers.** $$\text{HM}(A, B) = \frac{2}{\frac{1}{A} + \frac{1}{B}} = \frac{1}{3}$$ So $\frac{1}{A} + \frac{1}{B} = 6$. $$\text{HM}(C, D) = \frac{2}{\frac{1}{C} + \frac{1}{D}} = \frac{1}{5}$$ So $\frac{1}{C} + \frac{1}{D} = 10$. **Step 2: Compute HM of all four values A, B, C, D.** $$\text{HM}(A,B,C,D) = \frac{4}{\frac{1}{A} + \frac{1}{B} + \frac{1}{C} + \frac{1}{D}} = \frac{4}{6 + 10} = \frac{4}{16} = \frac{1}{4}$$ Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Nov. 20Question 3001 of 473

All Questions

The harmonic mean $\displaystyle A$ and $\displaystyle B$ is $\displaystyle 1/3$ and harmonic mean of $\displaystyle C$ and $\displaystyle D$ is $\displaystyle 1/5$ . The harmonic mean of $\displaystyle ABCD$ is

Options

\displaystyle 8/15

\displaystyle 1/4

\displaystyle 1/15

\displaystyle 5/3

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Correct Answer

✅ Option b — $\displaystyle 1/4$

All Options:

A $\displaystyle 8/15$
B $\displaystyle 1/4$
C $\displaystyle 1/15$
D $\displaystyle 5/3$

Detailed Solution & Explanation

**Step 1: Recall the formula for Harmonic Mean of two numbers.**

\text{HM}(A, B) = \frac{2}{\frac{1}{A} + \frac{1}{B}} = \frac{1}{3}

\displaystyle \frac{1}{A} + \frac{1}{B} = 6

\text{HM}(C, D) = \frac{2}{\frac{1}{C} + \frac{1}{D}} = \frac{1}{5}

\displaystyle \frac{1}{C} + \frac{1}{D} = 10

. **Step 2: Compute HM of all four values A, B, C, D.**

\text{HM}(A,B,C,D) = \frac{4}{\frac{1}{A} + \frac{1}{B} + \frac{1}{C} + \frac{1}{D}} = \frac{4}{6 + 10} = \frac{4}{16} = \frac{1}{4}

Hence, **Option B** 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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The harmonic mean A\displaystyle AA and B\displaystyle BB is 1/3\displaystyle 1/31/3 and harmonic mean of C\displaystyle CC and D\displaystyle DD is 1/5\displaystyle 1/51/5. The harmonic mean of ABCD\displaystyle ABCDABCD is