Question

Harmonic mean is

• A. Reciprocal of average of values of items of a series
• B. Reciprocal of average of reciprocal of values of items of a series
• C. Average of reciprocal of values of items of a series
• D. nth root of the product of values of items of a series

Hint:

Arithmetic Mean = Average of values; Geometric Mean = $n^{\text{th}}$ root of product; Harmonic Mean = Reciprocal of average of reciprocals.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Mathematical averages include Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM).

Step 2: Key Formula or Approach:
The Harmonic Mean (HM) of $n$ observations $x_1, x_2, \dots, x_n$ is mathematically defined as:
\[HM = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} = \frac{1}{\frac{1}{n} \sum_{i=1}^{n} \frac{1}{x_i}}\] This represents the reciprocal of the arithmetic mean of the reciprocals of the individual data values.

Step 3: Detailed Explanation:
Therefore, harmonic mean is the reciprocal of the average of the reciprocals of values of items of a series.

Step 4: Final Answer:
Hence, the correct option is (B).