Introduction to the Harmonic Mean Calculator
Harmonic mean calculator is a digital tool used to find a given number's harmonic average in a few seconds. It determines the average of the numbers whose values are divided by their sum value which is the reciprocal of each value in the given data.
Our harmonic means calculator is valuable for professionals, researchers, and students to solve different kinds of average problems with solutions for making assignments, notes, projects, etc. Our harmonic average calculator provides you with excellent results without involving you in the calculation of Harmonic means problems.
What is Harmonic Mean?
The harmonic mean is defined as the reciprocal sum of each observation that is divided by the total number of observations from the given number set. Thus it is an inverse method of the arithmetic mean method.
The harmonic mean is one of the complex methods from the Pythagorean theorem to find the average. Its real-life application is mostly in physics to calculate the average velocity, and density of alloys, and electrical resistances, and in finance in which the price and earnings average ratio.
Harmonic Mean Formula
The harmonic mean formula is based on the number of observations or the total number but is different from the regular mean formula.
In this formula, all the number of observation sum is written in ratio and n (total number divided by the sum ratio from the given set. The harmonic mean calculator uses the following formula to solve harmonic mean problems,
$$ \bar{x} \;=\; \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} \;=\; \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + … + \frac{1}{x_n}} $$
How to Calculate Harmonic Mean Using Harmonic Average Calculator
The harmonic mean calculation is a complex procedure even if you use its formula but still, it takes time to give you a solution to the harmonic mean problem. Let's see how to find the harmonic mean problem using some simple procedure. These steps are:
Step 1
Identify all the number of observations in the given set of data
Step 2
Take the reciprocal of each number of observations separately.
Step 3
Then add all the sum ratio numbers and add these values to the formula.
Step 4
Count the total number of observations n from the given data and add the n value
Step 5
After adding all the values in the formula, calculate the given values with the help of the harmonic means calculator and you will get the solution of the harmonic mean problem.
Let’s see an example of how to find harmonic mean by using our harmonic mean calculator. Sometimes you need to understand the manual calculations and for that, we are going to give you an example,
Example:
Find the harmonic mean of the data set (3,6,9):
Solution:
Here the number of observations is 3,6,9
Take the reciprocal of these observations which is
$$ \frac{1}{3}, \frac{1}{6}, \frac{1}{9} $$
Add these reciprocal
$$ \frac{1}{3} + \frac{1}{6} + \frac{1}{9} \;=\; \frac{11}{18} $$
As you can see n=3
Apply harmonic mean formula
$$ Harmonic\; mean \;=\; \frac{\frac{n}{1}}{x_1} + \frac{1}{x_2} + … + \frac{1}{x_n} $$
$$ H.M \;=\; \frac{\frac{3}{18}}{11} $$
$$ \frac{3 \times 11}{18} $$
$$ H.M \;=\; \frac{54}{11} $$
How to Use Harmonic Mean Calculator
Harmonic average calculator has an easy-to-use interface so that you can use it to calculate the complex average number value. Before calculating harmonic mean using different types of set data as input, you must follow some simple steps to avoid trouble during the calculation process. These steps are:
- Enter your number for the average numeric value in the input box.
- Review your input number values before hitting the calculate button to start the calculation process.
- Click on the “Calculate” button to get the desired result of your given harmonic mean problem
- If you want to try out our harmonic mean solver first then you can use the load example for a better understanding
- Click on the “Recalculate” button to get a new page for solving more number sets in the calculator.
Final Result of Harmonic Means Calculator
The harmonic mean calculator gives you the solution to a data set to find the average problem when you add the input to it. It provides you with solutions in a complete procedure. It may contain as:
- Result option
You can click on the result option and it provides you with a solution for harmonic mean problems
- Possible step
When you click on the possible steps option it provides you the solution and its calculation steps in detail.
Advantages of Harmonic Mean Solver
Harmonic mean calculator gives you tons of advantages whenever you use it to calculate numeric average value problems. These advantages are:
- Our tool saves your time and effort from doing complex calculations of harmonic mean value from the given data in a few seconds
- It is a free-of-cost tool so you can use it to solve average problems in harmonic average calculator.
- It is a versatile tool that allows you to solve the various types of set data in the harmonic means calculator
- You can use this calculator for practice to get a strong hold on the harmonic mean concept.
- It is a reliable tool that provides accurate solutions whenever you use it to calculate the given data for finding the harmonic average.
- It provides a solution with a complete process of harmonic mean in a step-by-step method so that you get more clarity.
