The HARMEAN() function returns the harmonic mean of a set data values. The syntax for the function is HARMEAN (number 1 , number 2, ....number_n). The arguments for the function "number 1, number 2.." can be a series of up to 30 values, an array, a referenced range of cells or a named range. Logical values will also be accepted when entered directly into the function however referenced cells that do not contain values or that cannot be converted to numeric values such as text, logical values or empty cells will be ignored. The HARMEAN function calculates the reciprocal of the arithmetic mean of reciprocals. For example: HARMEAN(3,2,4,5,) = 3.116883117 as the arithmetic mean of the reciprocals of the numbers 3,2,4,5 is (1/3+1/2+1/4+1/5)/4 = 0.3208333333 and the reciprocal of that is 1/0.320833333 = 3.116883117 The harmonic mean is a measure of the average of reciprocal values such that if the harmonic mean of a and c where the value b then 1/a, 1/b, 1/c would form an arithmetic progression (each term is created from the last by adding a constant). This is particularly usefully when working with average velocities over known distances or the average resistance of resistors in parallel. If the values of a = 2 and c=6 the arithmetic mean gives a result of 4 ( AVERAGE(2,6)=4 ) but the harmonic mean gives a result of 3 ( HARMEAN(2,6) = 3). This is because the arithmetic mean gives the number that falls an equal distance between two arguments on the number line. However the harmonic mean gives the reciprocal of the number that falls an equal distance between the reciprocals of the arguments on the n umber line. [number line 2,4,6 arithmetic mean] [number line 1/2,1/3,1/6 harmonic mean] The values 1/2, 1/3 and 1/6 have the same difference between them so they create a arithmetic progression. This progression is clearer when the value are written with the same denominator i.e. 3/6 , 2/6 , 1/6 where the common difference is 1/6 as calculated by the harmonic mean function. Note: The same cannot be said of the arithmetic mean. The values 1/2, 1/4 and 1/6 do NOT create an arithmetic progression. In general the harmonic mean is always smaller than the geometric or arithmetic mean. However they can be the same value when ALL the arguments are of equal value. To learn more about the uses of the harmonic mean see [The Harmonic Mean Mathematics Knoledgebase].

How to use the HARMEAN() function: Type " =HAREAN( " Enter the coordinate of the first data cell "A2" Type a colon. Enter the coordinate of the last data cell "A7" Type ")" then press the "Enter" key.

Note: All arguments for the HARMEAN function must be positive otherwise the function will return a #NUM! error value to the cell.