Measures of Central Tendency and DispersionMCQPYQ Nov. 20Question 3002 of 473

A fire engine rushes to a place of fire accident with a speed of $\displaystyle 110$ kmph and after the completion of operation returned to the base at a speed of $\displaystyle 55$ kmph. The average speed per hour in per-direction is obtained as ________ speeds.

Options

AAverage of

BH M of

CG M of

DHalf of HM of

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Correct Answer

✅ Option b — H M of

All Options:

AAverage of
BH M of
CG M of
DHalf of HM of

Detailed Solution & Explanation

**Step 1: Calculate average speed using the HM formula (for equal distances).** When the same distance is covered at two different speeds, the average speed is the Harmonic Mean of the two speeds:

\text{Average speed} = \frac{2 \times v_1 \times v_2}{v_1 + v_2} = \frac{2 \times 110 \times 55}{110 + 55} = \frac{12100}{165} = \frac{220}{3} \approx 73.33 \text{ km/hr}

**Step 2: Verify the GM.**

\text{GM} = \sqrt{110 \times 55} = \sqrt{6050} \approx 77.78 \text{ km/hr}

**Step 3: Correct answer.** The average speed over equal distances is the **HM** of the two speeds. The correct option should be **B** (HM of), not GM. Mathematically: Average speed = HM of the two speeds =

\displaystyle \frac{2 \times 110 \times 55}{110 + 55} = \frac{220}{3}

km/hr. 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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A fire engine rushes to a place of fire accident with a speed of 110\displaystyle 110110 kmph and after the completion of operation returned to the base at a speed of 55\displaystyle 5555 kmph. The average speed per hour in per-direction is obtained as ________ speeds.