3 Ways To Calculate The Harmonic Mean

For example, you may need to find the harmonic mean for the numbers 10, 12, 16, and 8.

For example, if you are finding the harmonic mean of the numbers 10, 12, 16, and 8, you are working with 4 values, the numerator of your formula will be 4:41a1+1a2+1a3+. . . +1an{\displaystyle {\frac {4}{{\frac {1}{a_{1}}}+{\frac {1}{a_{2}}}+{\frac {1}{a_{3}}}+. . . +{\frac {1}{a_{n}}}}}}

For example, if the values in your set are 10, 12, 16, and 8, you would place the fractions 110{\displaystyle {\frac {1}{10}}}, 112{\displaystyle {\frac {1}{12}}}, 116{\displaystyle {\frac {1}{16}}}, 18{\displaystyle {\frac {1}{8}}} in your denominator:4110+112+116+18{\displaystyle {\frac {4}{{\frac {1}{10}}+{\frac {1}{12}}+{\frac {1}{16}}+{\frac {1}{8}}}}}

For example:4110+112+116+18=489240{\displaystyle {\frac {4}{{\frac {1}{10}}+{\frac {1}{12}}+{\frac {1}{16}}+{\frac {1}{8}}}}={\frac {4}{\frac {89}{240}}}}

For example:489240{\displaystyle {\frac {4}{\frac {89}{240}}}}=4×24089{\displaystyle =4\times {\frac {240}{89}}}=41×24089{\displaystyle ={\frac {4}{1}}\times {\frac {240}{89}}}=96089{\displaystyle ={\frac {960}{89}}}

For example:96089{\displaystyle {\frac {960}{89}}}=960÷89{\displaystyle =960\div 89}=10. 79{\displaystyle =10. 79}So, the harmonic mean of the numbers 10, 12, 16, and 8 is 10. 79.

For example, if you need to find the harmonic mean of 10, 12, 16, and 8, you might type each of these values into a separate cell in the spreadsheet, cells A1-A4.

For example, type “=HARMEAN” into cell A5 of your spreadsheet and double-click on the function.

For example, highlight cells A1-A4 of your spreadsheet and hit enter. Excel will calculate 10. 78652 as the harmonic mean.