Measures of Central Tendency and DispersionMCQMTP May 19Question 3052 of 473

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

Options

\displaystyle AM \geq GM \geq HM

\displaystyle HM \geq GM \geq AM

\displaystyle AM > GM > HM

\displaystyle GM > AM > HM

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Correct Answer

✅ Option c — $\displaystyle AM > GM > HM$

All Options:

A $\displaystyle AM \geq GM \geq HM$
B $\displaystyle HM \geq GM \geq AM$
C $\displaystyle AM > GM > HM$
D $\displaystyle GM > AM > HM$

Detailed Solution & Explanation

**Step 1: Recall the inequality of means.** For a set of **distinct** positive observations, the strict inequality holds:

\text{AM} > \text{GM} > \text{HM}

**Step 2: Match with options.** - Option A: AM ≥ GM ≥ HM — true in general (equality when all equal), but for distinct positive observations, strict inequality holds. - Option C: AM > GM > HM — this is correct for distinct positive observations. - Option B: HM ≥ GM ≥ AM — this is **wrong** (reverses the order). **Correct answer:** For distinct positive observations, AM > GM > HM = **Option C**. Note: The exam key says B, which is mathematically incorrect. The correct answer is **C**. 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.

Related Comparison Tables

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