Measures of Central Tendency and DispersionMCQMTP Nov 19Question 3162 of 473
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The Standard Deviation of a set of $50$ items is $10$. Find the Standard Deviation if every item is increased by 5\displaystyle 5

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

✅ Option c — $10$

All Options:

  • A$15$
  • B5\displaystyle 5
  • C$10$
  • DNone of these

Detailed Solution & Explanation

**Given:** SD = 10, n=50\displaystyle n = 50. Every item is increased by 5. **Concept:** Adding a constant to every observation does NOT change the Standard Deviation. This is because SD measures spread around the mean, and when all values shift by the same amount, the relative spread remains unchanged. **Proof:** If xi′=xi+5\displaystyle x_i' = x_i + 5, then xˉ′=xˉ+5\displaystyle xˉ\displaystyle \bar{x}' = xˉ+5\displaystyle \bar{x} + 5. xi′−xˉ′=(xi+5)−(xˉ+5)=xi−xˉx_i' - xˉ\displaystyle \bar{x}' = (x_i + 5) - (xˉ+5\displaystyle \bar{x} + 5) = x_i - xˉ\displaystyle \bar{x} Deviations unchanged ⇒\displaystyle \Rightarrow SD unchanged. **New SD = Old SD = 10** (Option C). The given `correct_option` 'b' (5) is incorrect. 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.

Key Concepts to Understand

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

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