Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IQuestion 2922 of 473
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The mean salary of a group of $50$ persons is Rs. $5850$. Later on it is discovered that the salary of one has been wrongly taken as Rs. $8000$ instead of Rs. $7500$. The corrected mean salary is

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

✅ Option d — None of these

All Options:

  • ARs. $5854$
  • BRs. $5846$
  • CRs. $5640$
  • DNone of these

Detailed Solution & Explanation

**Step 1: Original (wrong) total sum.** Wrong sum=50×5850=292500Wrong sum=50\displaystyle \text{Wrong sum} = 50 ×\displaystyle \times 5850 = 292500 **Step 2: Correct the sum.** Correct sum=292500−8000+7500=292000Correct sum=292500−8000+7500=292000\displaystyle \text{Correct sum} = 292500 - 8000 + 7500 = 292000 **Step 3: Compute correct mean.** Correct mean=29200050=5840Correct mean=29200050=5840\displaystyle \text{Correct mean} = \frac{292000}{50} = 5840 **Note:** The correct mean is **Rs. 5840**. Looking at the options: Option C is Rs. 5640, Option B is Rs. 5846, neither matches exactly. However 5840 is not among options A, B, C exactly. The `correct_option` is D (None of these), but 5840 is very close to but not the same as any option. Given these options, **D (None of these)** is technically the correct choice since 5840 ≠ 5854, 5846, or 5640. Hence, **Option D** 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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