Central Tendency & DispersionMTP May 19Question 3052 of 473
All Questions

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

Options

AAM≥GM≥HM\displaystyle AM \geq GM \geq HM
BHM≥GM≥AM\displaystyle HM \geq GM \geq AM
CAM>GM>HM\displaystyle AM > GM > HM
DGM>AM>HM\displaystyle GM > AM > HM
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Correct Answer

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

All Options:

  • AAM≥GM≥HM\displaystyle AM \geq GM \geq HM
  • BHM≥GM≥AM\displaystyle HM \geq GM \geq AM
  • CAM>GM>HM\displaystyle AM > GM > HM
  • DGM>AM>HM\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: AM>GM>HM\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.

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