Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 3068 of 473
All Questions

Which of the following result hold for a set of distinct positive observations?

Options

AA.M. >\displaystyle > G.M. >\displaystyle > H.M.
BG.M. >\displaystyle > A.M. >\displaystyle > H.M.
CG.M. >\displaystyle > H.M. >\displaystyle > A.M.
DG.M. >\displaystyle > A.M. >\displaystyle > H.M.
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Correct Answer

✅ Option a — A.M. >\displaystyle > G.M. >\displaystyle > H.M.

All Options:

  • AA.M. >\displaystyle > G.M. >\displaystyle > H.M.
  • BG.M. >\displaystyle > A.M. >\displaystyle > H.M.
  • CG.M. >\displaystyle > H.M. >\displaystyle > A.M.
  • DG.M. >\displaystyle > A.M. >\displaystyle > H.M.

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Detailed Solution & Explanation

**Step 1: Recall the inequality of means.** For a set of distinct positive numbers: AM>GM>HM\text{AM} > \text{GM} > \text{HM} (Equality holds only when all numbers are equal; for distinct numbers, strict inequality.) **Step 2: Match with options.** - **Option A:** A.M. > G.M. > H.M. ✓ — This is the correct inequality. 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.

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.

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