Learn Harmonic Mean Online

Introduction to learn harmonic mean online:
Harmonic mean is used to find the average of the given terms. Harmonic mean is defined as the number of given value divided by the inverse of the each values given. For calculating the harmonic mean, we are using one of the formula. By using the formula, we are calculating the harmonic mean.


Explanation to learn harmonic mean online

The explanations to learn harmonic mean is as follows,

Online has number of examples about the harmonic mean with suitable solutions.
All the examples given in online are worked out with step by step solutions.
Also the practice problems for the harmonic mean are very helpful to the students.
The formula given for calculating the harmonic mean is as follows,

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3) + .......(1/a_n))`

Where,

N = Number of terms in the given functions.
`1/a_1`   = Inverse of each terms in the given functions. Understanding Interesting Data Sets is always challenging for me but thanks to all math help websites to help me out.

Example problems to learn harmonic mean online

Problem to learn in online:

Problem 1:  2, 4, 8, 16. What is the value of the harmonic mean?.

Solution:

Step 1: Given:

Data  = 2, 4, 8, 16

N = 4

Step 2: Formula:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3)....(1/a_n))`

Step 3: Simplify:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3) + (1/a_4) )`

= `4/ ( (1/2) + ( 1/4) + (1/8) + (1/16))`

Step 4: Solve:

=  `4/((8 + 4 + 2 + 1)/16)`

= `64/(8 + 4 + 2 + 1)`

= `64/15`

= 4.2666

Result: Harmonic Mean = 4.2666

Thus, this is the required answer for the above given harmonic function.

Problem 2: 1, 3, 6, 8, 12. What is the value of the harmonic mean?.

Solution:

Step 1: Given:

Data  = 1, 3, 6, 8, 12

N = 5

Step 2: Formula:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3)....(1/a_n))`

Step 3: Simplify:

Harmonic Mean =  `N/( (1/a_1) + (1/a_2) + (1/a_3) + (1/a_4) )`

= `5/ ( (1/1) + ( 1/3) + (1/6) + (1/8) + (1/12))`

Step 4: Solve:

=  `5/((24 + 8 + 4 + 3+ 2)/24)`

= `5/((41/24))`

= `120/41`

= 2.9268

Result: Harmonic Mean = 2.9268


Practice problems to learn harmonic mean online

Practice problems to learn in online:

Problem 1: 2, 6, 12, 24, 26. What is the value of the harmonic mean?

Answer: 6.027

Problem 2: 3, 5, 7, 9, 12. What is the value of the harmonic mean?

Answer: 5.742