Measures of Central Tendency and DispersionMCQMTP Nov 19Question 2889 of 473
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The average weight of 8 person increases by 1.5 kg, if a person weighing 65 kg replaced by a new person, what would be the weight of the new person?

Options

A76 kg
B80 kg
C77 kg
DNone of these
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Correct Answer

✅ Option c — 77 kg

All Options:

  • A76 kg
  • B80 kg
  • C77 kg
  • DNone of these

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Detailed Solution & Explanation

**Step 1: Understand the effect of replacement on the average.** When the average of 8 persons increases by 1.5 kg, the total weight increases by 8×1.5=12\displaystyle 8 \times 1.5 = 12 kg. **Step 2: Compute the weight of the new person.** Total weight increase =\displaystyle = Weight of new person −\displaystyle - Weight of replaced person 12=Wnew−6512 = W_{new} - 65 Wnew=65+12=77 kgW_{new} = 65 + 12 = 77 \text{ kg} **Note:** The computed weight is 77 kg (Option C), not 76 kg (Option A). Let us verify: increase in average =1.5\displaystyle = 1.5 kg, n=8\displaystyle n = 8 persons, total increase =12\displaystyle = 12 kg. New person's weight =65+12=77\displaystyle = 65 + 12 = 77 kg. 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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