Measures of Central Tendency and DispersionMCQMTP Dec 22 Series IQuestion 2911 of 473
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The mean of $100$ students was $45$. Later, it was discovered that the marks of two students were misread as $85\displaystyle and $54 instead of $58\displaystyle and $45. Find correct mean.

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

✅ Option c — 44.64

All Options:

  • A68
  • B36
  • C44.64
  • D52

Detailed Solution & Explanation

**Step 1: Compute the original total sum.** Wrong sum=100×45=4500Wrong sum=100\displaystyle \text{Wrong sum} = 100 ×\displaystyle \times 45 = 4500 **Step 2: Correct the sum.** Wrong readings: 85 and 54 (sum = 139). Correct readings: 58 and 45 (sum = 103). Correct sum=4500−139+103=4500−36=4464Correct sum=4500−139+103=4500−36=4464\displaystyle \text{Correct sum} = 4500 - 139 + 103 = 4500 - 36 = 4464 **Step 3: Compute correct mean.** Correct mean=4464100=44.64Correct mean=4464100=44\displaystyle \text{Correct mean} = \frac{4464}{100} = 44.64 **Note:** The correct mean is **44.64** (Option C), not 68 (Option A). 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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