Correct Answer: Correct answer is: (A) The reciprocal of the arithmetic average of the reciprocals of the values of its various items.
Exam Relevance: GRE, GMAT, CAT, SAT
Difficulty: Easy
Concept notes: The harmonic mean is a type of average that is calculated by taking the reciprocal of the arithmetic mean of the reciprocals of the data points.
Common Mistakes: Students often confuse the harmonic mean with the arithmetic mean or the geometric mean, leading to incorrect calculations.
Explanations: The harmonic mean is defined as the reciprocal of the arithmetic average of the reciprocals of the values. This means that for a set of values \( x_1, x_2, \ldots, x_n \), the harmonic mean \( H \) is given by: \[ H = \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + \frac{1}{x_n}} \] This formula ensures that the harmonic mean is always less than or equal to the arithmetic mean, and it is particularly useful for averaging rates or ratios.
Option Analysis: - Option A: Correct. This is the definition of the harmonic mean.
- Option B: Incorrect. This describes the arithmetic mean, not the harmonic mean.
- Option C: Incorrect. The harmonic mean is well-defined for positive values.
- Option D: Incorrect. This is not the correct definition.
Mnemonic: Reciprocal Average Reciprocal (RAR)
Ques 51 explanation is not related to the question…
Very useful question but plz give explanation with correct answer