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Which of the following results hold for a set of distinct positive observations?
- a)AM ≥ GM ≥ HM
- b)HM ≥ GM ≥ AM
- c)AM > GM > HM
- d)GM > AM > HM
Correct answer is option 'C'. Can you explain this answer?
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Which of the following results hold for a set of distinct positive obs...
B)GM ≥ HM
The correct answer is b) GM ≥ HM.
AM (Arithmetic Mean), GM (Geometric Mean), and HM (Harmonic Mean) are three measures of central tendency used for a set of observations.
For a set of distinct positive observations, it is true that:
AM = (sum of observations) / (number of observations)
GM = (product of observations)^(1/number of observations)
HM = (number of observations) / (sum of (1/observations))
It can be shown that for any set of positive observations, AM ≥ GM ≥ HM. However, for a set of distinct positive observations, the equality AM = GM = HM holds only when all the observations are equal.
Therefore, the correct answer is b) GM ≥ HM.
The correct answer is b) GM ≥ HM.
AM (Arithmetic Mean), GM (Geometric Mean), and HM (Harmonic Mean) are three measures of central tendency used for a set of observations.
For a set of distinct positive observations, it is true that:
AM = (sum of observations) / (number of observations)
GM = (product of observations)^(1/number of observations)
HM = (number of observations) / (sum of (1/observations))
It can be shown that for any set of positive observations, AM ≥ GM ≥ HM. However, for a set of distinct positive observations, the equality AM = GM = HM holds only when all the observations are equal.
Therefore, the correct answer is b) GM ≥ HM.
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