Measures of Central Tendency and DispersionMCQPYQ May 18Question 2854 of 473
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If each item is reduced by 15 A. M is

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

✅ Option a — Reduced by 15

All Options:

  • AReduced by 15
  • BIncreased by 15
  • CReduced by 10
  • DNone of these

Detailed Solution & Explanation

**Step 1: Recall the effect of subtracting a constant from each observation.** Let the original observations be x1,x2,…,xn\displaystyle x_1, x_2, \ldots, x_n with mean xˉ\displaystyle xˉ\displaystyle \bar{x}. New observations: xi′=xi−15\displaystyle x_i' = x_i - 15 for each i\displaystyle i. **Step 2: Compute the new mean.** xˉ′=∑(xi−15)n=∑xin−15=xˉ−15xˉ\displaystyle \bar{x}' = \displaystyle \frac{\sum (x_i - 15)}{n} = \frac{∑\displaystyle \sum x_i}{n} - 15 = xˉ−15\displaystyle \bar{x} - 15 **Step 3: Conclusion.** The new A.M. is xˉ−15\displaystyle xˉ−15\displaystyle \bar{x} - 15, i.e., reduced by 15. Hence, **Option A** 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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