What is Harmonic Mean?

When three numbers are in harmonic progression, the middle number is called the Harmonic mean of the other two numbers.

For example, if a, b and c are in harmonic progression, the middle number c is called the harmonic mean of a and b.

What is the formula for calculating Harmonic mean?

The formula for calculating harmonic mean cannot be directly obtained by taking a harmonic progression. It is obtained by taking the reciprocals of a harmonic progression, which gives us an arithmetic progression. Then it becomes easier to calculate the harmonic mean as described below:

Let three numbers a, b and c be in harmonic progression. Hence b is the harmonic mean between a and b. Now, the reciprocals of these numbers,

Now, since 1/b is the arithmetic mean between 1/a and 1/c, thus

On solving the above equation, we get

Formula for harmonic mean (explained below) |

For example, if a, b and c are in harmonic progression, the middle number c is called the harmonic mean of a and b.

What is the formula for calculating Harmonic mean?

The formula for calculating harmonic mean cannot be directly obtained by taking a harmonic progression. It is obtained by taking the reciprocals of a harmonic progression, which gives us an arithmetic progression. Then it becomes easier to calculate the harmonic mean as described below:

Let three numbers a, b and c be in harmonic progression. Hence b is the harmonic mean between a and b. Now, the reciprocals of these numbers,

1/a, 1/b, 1/care in arithmetic progression (because a harmonic progression is defined as the sequence of numbers obtained by taking the reciprocals of each number of an arithmetic progression)

Now, since 1/b is the arithmetic mean between 1/a and 1/c, thus

1/b = (1/a + 1/c)/2(the above result is obtained by the formula for arithmetic mean)

On solving the above equation, we get

b = 2ac/(a + c)Therefore the formula for harmonic mean between two numbers a and c is

b = 2ac/(a + c), where b is the harmonic mean between a and cRelated posts:

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