CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
For the two unequal positive observations 4 and 16, which of the following relationships among the three means is correct?
The correct relationship is HM < GM < AM. For 4 and 16, the arithmetic mean is 10, the geometric mean is 8 and the harmonic mean is 6.4. This ordering holds for any set of unequal positive observations.
- AGM < HM < AM
- BAM < GM < HM
- CHM < GM < AMCorrect
- DGM < AM < HM
Explanation
AM = (4+16)/2 = 10. GM = √64 = 8. HM = 2 × 64 / 20 = 6.4. Hence HM < GM < AM. For unequal positive values this ordering always holds, and the three means are equal only when all observations are identical.
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