Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 2913 of 473
All Questions

The mean of 100\displaystyle 100 observations is 50\displaystyle 50. If one of the observations which was 50\displaystyle 50 is replaced by 40\displaystyle 40, the resulting mean will be:

Options

A40
B49.90
C30
DNone of these
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Correct Answer

✅ Option b — 49.90

All Options:

  • A40
  • B49.90
  • C30
  • DNone of these

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Detailed Solution & Explanation

**Step 1: Original total sum.** Sum=100×50=5000\text{Sum} = 100 \times 50 = 5000 **Step 2: New sum after replacement.** New sum=5000−50+40=4990\text{New sum} = 5000 - 50 + 40 = 4990 **Step 3: New mean.** New mean=4990100=49.90\text{New mean} = \frac{4990}{100} = 49.90 **Note:** The computed new mean is **49.90** (Option B), not 40 (Option A). 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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