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!
To compute a harmonic mean of a list of values, count the total number $ n ofvaluesinthelistandcalculatethesum 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,takingthedistance 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.
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.
The harmonic series is the sequence of inverses of non-zero natural numbers denoted Hn
$$ H_n = 1 + \frac12 + \frac13 + \frac14 + \cdots + \frac1n = \sum_{k=1}^n \frac1k $$
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.
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 2025-01-09,