Central Tendency & DispersionPYQ Dec 21Question 3031 of 473
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If the AM and GM for 10 observations are both 15, then the value of HM is

Options

ALess than 15
BMore than 15
C15
DCannot be determined
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Correct Answer

✅ Option c — 15

All Options:

  • ALess than 15
  • BMore than 15
  • C15
  • DCannot be determined

Detailed Solution & Explanation

**Step 1: Recall the relationship AM × HM = GM².** GM2=AM×HM\text{GM}^2 = \text{AM} \times \text{HM} **Step 2: Substitute given values.** - AM = 15, GM = 15 152=15×HM15^2 = 15 \times \text{HM} 225=15×HM225 = 15 \times \text{HM} HM=15\text{HM} = 15 **Step 3: Verify using the inequality AM ≥ GM ≥ HM.** Equality holds when all observations are equal. Since AM = GM = 15, all 10 observations must be equal to 15, which means HM = 15 as well. **Conclusion:** HM = 15. Hence, **Option C** is the correct answer.

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