# harmonic mean calculator

This online Harmonic Mean Calculator calculates the harmonic mean of a set of positive real numbers. [1] Matthews, G. (2004) "Fairness Opinions: Common Errors and Omissions." In this case, all of the numbers are divisible by 120. McGraw Hill. The harmonic mean of the given number is the ratio of the number of observations to the sum of the reciprocal of the given numbers. Please note that the values of the given sample should be input in the form separated by semicolon. We are not to be held responsible for any resulting damages from proper or improper use of the service. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. The formula for calculating the harmonic mean of a set of non-zero positive numbers is: where n is number of items and X1…X2 are the numbers from 1 to n. To put it simply, all you need to do is divide the number of items in the set by the sum of their reciprocals. The different types of progressions are arithmetic progression, geometric progression and the harmonic progression. The geometric mean, often referred to as the geometric average, is a so-called specialized average and is defined as the n-th root of the product of n numbers of the same sign. Let's say the distance from A to B is 120 km. BYJU’S online harmonic mean calculator tool performs the calculation faster, and it displays the harmonic mean in a fraction of seconds. The harmonic mean is more complex to solve than the arithmetic, although they might seem similar at first. The equation for finding the average speed is: Average speed = total distance/ total time, Average speed = 2 x 120/(120/80 + 120/60) = 240/3.5 = 68.6 km/h. The procedure to use the harmonic mean calculator is as follows: Step 1: Enter the numbers separated by a comma in the input field, Step 2: Now click the button “Solve” to get the harmonic mean, Step 3: Finally, the harmonic mean for the given numbers will be displayed in the output field. Harmonic Mean Calculator How to use this calculator. If you're given the set of numbers: 3, 12, 20, 24, and have to find their harmonic mean, the first thing you should do is find a common denominator. It is one of the three Pythagorean means that provides the most accurate average. For example, in computer sciences the harmonic mean is used to calculate the aggregate score for the evaluation of performance of machines, algorithms, and systems. The different types of progressions are arithmetic progression, geometric progression and the. Our harmonic mean calculator does the math for you! Alternatively they may be entered on separate lines. The index you have to calculate is made up of the three stocks: 60% invested in the first company, 25% in the second, and 15% invested in the third. The two ladders cross at a height H from the ground. You just need to write down the number dataset, separating the items with a comma and a blank space. Its P/E ratio, found using the weighted harmonic mean, is: P/E = (0.6 + 0.25 + 0.15)/ 0.6/10 + 0.25/9 + 0.15/50 = 1/ 0.09 = 11.1. Harmonic Mean Calculator Mean Calculator Median Calculator Mode Calculator. In this case, the harmonic mean of A and B is twice as big as H. Given the fact that the harmonic average is the most precise one, it is no surprise it has found its way into many sciences. Harmonic Mean - Calculator Enter all … There are a few theorems regarding the usage of the harmonic mean in geometry: You can use this calculator to solve any of the above problems. The harmonic mean is one of the three Pythagorean means, involving in many situations where rates, ratios, geometry, trigonometry etc considered, the harmonic mean provides the truest average. All numbers must be positive and must be separated by commas or spaces. The harmonic mean of the given number is the ratio of the number of observations to the sum of the reciprocal of the given numbers. [2] Roger Voles. [3] Richinick, J. (1999) "Integer solutions of a-2 + b-2 = d-2", Mathematical Gazette, 83, p. 269-271. In biology, more precisely in population genetics, the harmonic average is a means of calculating the fluctuation effects on generation size. The semi-latus rectum in an ellipse K is equal to the harmonic average of the minimum and maximum distances of K from a focus; In a trapezoid ABCD where AB and CD are parallel sides, the diagonals AC and BD intersect at point E. If point F lies on AD, and point G lies on BC, so that FEG is parallel to AB and CD, then FG is equal to the harmonic mean of AB and CD. The harmonic mean formula is given as: Your email address will not be published. For example, 2, 3, 4 are the given set of numbers, then the harmonic mean is calculated as: Harmonic mean = 3 /[(1/2) + (1/3)+ (1/4)], Your email address will not be published. You can verify the above result in the calculator. In terms of its calculation, it is essentially the reciprocal of the average of the reciprocal values in the sample. How does this harmonic mean calculator work? The harmonic mean is in relation to the arithmetic mean (A = (X1 + X2)/2) and the geometric mean (G = √X1 x X2) in the following manner: Since in a set of real, non-negative numbers the arithmetic is always greater than the geometric mean, we can conclude that when n = 2, the harmonic mean will always be lesser in value or equal to the geometric mean (H ≤ G).

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