Measures of Central Tendency and DispersionMCQPYQ Nov 18Question 2856 of 473
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The mean of 20 items of a data is 5 & if each item is multiplied by 3, then the new mean will be

Options

A5\displaystyle 5
B10\displaystyle 10
C15\displaystyle 15
D20\displaystyle 20
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Correct Answer

✅ Option c — 15\displaystyle 15

All Options:

  • A5\displaystyle 5
  • B10\displaystyle 10
  • C15\displaystyle 15
  • D20\displaystyle 20

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Detailed Solution & Explanation

**Step 1: State the given information.** Number of items n=20\displaystyle n = 20, Original mean xˉ=5\displaystyle \bar{x} = 5. **Step 2: Apply the property of mean under multiplication.** If each item xi\displaystyle x_i is multiplied by a constant k\displaystyle k, the new mean becomes k⋅xˉ\displaystyle k \cdot \bar{x}. Here k=3\displaystyle k = 3, so: New mean=3×xˉ=3×5=15\text{New mean} = 3 \times \bar{x} = 3 \times 5 = 15 **Step 3: Verification.** Original sum =n×xˉ=20×5=100\displaystyle = n \times \bar{x} = 20 \times 5 = 100. New sum =3×100=300\displaystyle = 3 \times 100 = 300. New mean =30020=15\displaystyle = \frac{300}{20} = 15. ✓ 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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