HARMEAN

Returns the harmonic mean of the arguments.

Syntax:

HARMEAN(number1, number2, ... number30)

number1 to number30 are up to 30 numbers or ranges containing numbers. Numbers must not be zero.

The harmonic mean of $a_1,a_2,\dots a_n$ is defined as.

$\frac{n}{{\sum }_{i=1}^n\frac{1}{a_i}}$

Example:

HARMEAN(2, 4, 4)

returns 3, calculated as 3/(1/2 + 1/4 + 1/4).

To get a fair representation of the average efficiency, you should use the harmonic mean. The harmonic mean is particularly useful in this scenario because it gives more weight to lower values, which is important when evaluating rates or ratios like efficiency. A low efficiency on one day (e.g., a rainy day) can significantly impact the overall performance, and the harmonic mean accounts for this better than a simple arithmetic mean.

The HARMEAN function is used to calculate this value.

The formula for the harmonic mean is:

$H=\frac{n}{{\sum }_{i=1}^n\frac{1}{x_i}}$

Where:

• H is the harmonic mean.
• n is the number of data points.
• xi​ are the individual data points.

Using the data from the table:

n=4

x1​=22.5

x2​=21

x3​=18

x4​=15.5

The calculation would be:

$HARMEAN(22.5,21.0,18.0,15.5)=\frac{4}{\frac{1}{22.5}+\frac{1}{21.0}+\frac{1}{18.0}+\frac{1}{15.5}}$

$=\frac{4}{0.0444+0.0476+0.0556+0.0645}$

$=\frac{4}{0.2121}$

$=18.86$

The harmonic mean efficiency of the solar panels is approximately 18.86%. This value is a more realistic representation of the panel's average performance, as it is lower than the arithmetic average (which would be around 19.25%) and properly accounts for the impact of lower efficiency on rainy days.