Measures of Central Tendency and DispersionMCQMTP Dec 22 - Series IQuestion 3019 of 473
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A train covered the first 5 km\displaystyle 5  km\displaystyle \text{ km} of its journey at a speed of $30 km/hr<span\displaystyle \text{km/hr}<span class="katex-error" title="ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 30: …, and the next &̲#36;15 \text{ k…" style="color:#cc0000">\displaystyle , and the next &#36;15  km\displaystyle \text{ km} at a speed of $45 km/hr\displaystyle \text{km/hr}$. The average speed of the train was:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — $40 \text{ km/hr}$

All Options:

  • A$38 \text{ km/hr}$
  • B$40 \text{ km/hr}$
  • C$36 \text{ km/hr}$
  • D$42 \text{ km/hr}$

Detailed Solution & Explanation

**Step 1: Calculate total distance.** Total distance=5+15=20 kmTotal distance=5+15=20\displaystyle \text{Total distance} = 5 + 15 = 20  km\displaystyle \text{ km} **Step 2: Calculate time for each part.** - Time for first 5 km at 30 km/hr: t1=530=16\displaystyle t_1 = 530=16\displaystyle \frac{5}{30} = \frac{1}{6} hr - Time for next 15 km at 45 km/hr: t2=1545=13\displaystyle t_2 = 1545=13\displaystyle \frac{15}{45} = \frac{1}{3} hr **Step 3: Calculate total time.** ttotal=16+13=16+26=36=12 hrt_{total\displaystyle \text{total}} = 16+13=16+26=36=12\displaystyle \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}  hr\displaystyle \text{ hr} **Step 4: Calculate average speed.** vˉ=Total distanceTotal time=201/2=40 km/hr\displaystyle \bar{v} = \frac{Total distance\displaystyle \text{Total distance}}{Total time\displaystyle \text{Total time}} = 201/2=40\displaystyle \frac{20}{1/2} = 40  km/hr\displaystyle \text{ km/hr} The average speed is $40$ km/hr = **Option B**. Note: The exam key says Option D ($42\displaystyle km/hr), but the correct calculation gives &#36;40 km/hr (Option B). 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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