Question

Find the harmonic mean of the following numbers: 5, 10, 15

• A. 10
• B. 8.18
• C. 15
• D. 9.08

Hint:

To calculate the harmonic mean, take the reciprocal of each number, find the sum, and then take the reciprocal of the result.

Answer 1

The Correct Option is B

The formula for the harmonic mean (H.M.) of \( n \) numbers \( x_1, x_2, \ldots, x_n \) is: \[ \text{H.M.} = \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + \frac{1}{x_n}} \] For the given numbers 5, 10, and 15, the harmonic mean is: \[ \text{H.M.} = \frac{3}{\frac{1}{5} + \frac{1}{10} + \frac{1}{15}} = \frac{3}{\frac{6 + 3 + 2}{30}} = \frac{3}{\frac{11}{30}} = \frac{3 \times 30}{11} = \frac{90}{11} \approx 8.18 \]