Enter a set of numbers to calculate the harmonic mean.
The harmonic mean is a specialized type of average used to describe the overall characteristics of a data set, particularly for rates like speed or efficiency. It is calculated by taking the reciprocal of the average of the reciprocals of the numbers in the data set. The formula is: \( H = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} \) Where: \( n \) is the total number of values, \( x_i \) is each individual value.
Steps:
Solution:
Reciprocals:
\( \frac{1}{100} = 0.01 \), \( \frac{1}{200} = 0.005 \), \( \frac{1}{300} = 0.003333 \), \( \frac{1}{400} = 0.0025 \), \( \frac{1}{500} = 0.002 \)
Sum of reciprocals:
\( \frac{1}{100} + \frac{1}{200} + \frac{1}{300} + \frac{1}{400} + \frac{1}{500} = 0.01 + 0.005 + 0.0033333 + 0.0025 + 0.002 \approx 0.0228333 \)
Harmonic mean:
\( H = \frac{5}{0.0228333} \approx 218.9781 \)
Solution:
Reciprocals:
\( \frac{1}{60} \approx 0.01667 \), \( \frac{1}{120} \approx 0.00833 \), \( \frac{1}{180} \approx 0.00556 \)
Sum of reciprocals:
\( \frac{1}{60} + \frac{1}{120} + \frac{1}{180} \approx 0.01667 + 0.00833 + 0.00556 \approx 0.03056 \)
Harmonic mean:
\( H = \frac{3}{0.03056} \approx 98.18 \)