Tool for calculating a harmonic mean from a series or list of integers or real numbers. The harmonic mean is for example used for average speeds.
Harmonic Mean - dCode
Tag(s) : Statistics
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Harmonic Mean
Harmonic Mean Calculator
Answers to Questions (FAQ)
How to compute an harmonic mean? (Definition)
With a list $ X $ of n values/numbers $ \{x_1, x_2, \dots, x_n \} $. The harmonic mean is defined by the ratio/division of $ n $ by the sum of the inverse of the values/numbers:
$$ \bar{x}_{harm} = \frac{n}{\sum_{i=1}^n \frac{1}{x_i}} $$
How to compute an harmonic mean?
To compute a harmonic mean of a list of values, count the total number $ n $ of values in the list and calculate the sum $ S $ of the inverse values.
Example: A car drove a distance $ d $ at 30km/h half the distance then to 90km/h. The average speed of the car can be defined with its harmonic mean speed by the calculation $ n/S $ with $ n = 2 $ and $ S = 1/30 + 1/90 = 0.0444... $ so $ \bar{M}_{harm} = 2/(1/30+1/90) = 45 $ km/h.
Indeed, taking the distance $ d = 15km $, the car will have traveled $ d/2 $ at 30km/h in 15 minutes and $ d/2 $ at 90km/h in 5 minutes, so a total distance of 15km in 20 minutes or 45km/h on average.
When to use an harmonic mean?
The harmonic mean is used when the compared elements have inverse proportionality ratios.
Example: The price per square meter of a house is higher if the total area is small.
Example: Travel time is shorter when the speed is high.
What is the harmonic series? (Definition)
The harmonic series is the sequence of inverses of non-zero natural numbers denoted $ H_n $
$$ H_n = 1 + \frac12 + \frac13 + \frac14 + \cdots + \frac1n = \sum_{k=1}^n \frac1k $$
Source code
dCode retains ownership of the "Harmonic Mean" source code. Except explicit open source licence (indicated Creative Commons / free), the "Harmonic Mean" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Harmonic Mean" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Harmonic Mean" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Harmonic Mean" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Harmonic Mean on dCode.fr [online website], retrieved on 2024-11-21,
