What is the formula of harmonic mean?

What is the formula of harmonic mean?

The harmonic mean is a type of numerical average. It is calculated by dividing the number of observations by the reciprocal of each number in the series. Thus, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. The harmonic mean of 1, 4, and 4 is: 3 ( 1 1 + 1 4 + 1 4 ) = 3 1 .

How do you find the harmonic mean in statistics?

The general formula for calculating a harmonic mean is:

  1. Harmonic mean = n / (∑1/x_i)
  2. Weighted Harmonic Mean = (∑w_i ) / (∑w_i/x_i)
  3. P/E (Index) = (0.4+0.6) / (0.4/50 + 0.6/4) = 6.33.
  4. P/E (Index) = 0.4×50 + 0.6×4 = 22.4.

Can harmonic mean be negative?

The harmonic mean does not take rates with a negative or zero value, e.g. all rates must be positive.

How harmonic mean differ from arithmetic mean?

The harmonic mean is the inverse of the arithmetic mean of the inverses. The arithmetic mean is the inverse of the harmonic mean of the inverses. So, each one thinks of the other in the same way, if you will, so, psychologically there is no difference.

Why harmonic mean is used in F1 score?

The F1 score is the harmonic mean of precision and recall taking both metrics into account in the following equation: We use the harmonic mean instead of a simple average because it punishes extreme values. A classifier with a precision of 1.0 and a recall of 0.0 has a simple average of 0.5 but an F1 score of 0.

What is geometric mean and harmonic mean in statistics?

Geometric and Harmonic Mean The geometric mean (G.M.) and the harmonic mean (H.M.) forms an important measure of the central tendency of data. They tell us about the central value of the data about which all the set of values of data lies.

How harmonic mean is different from geometric mean?

So just as the harmonic mean is simply the arithmetic mean with a few reciprocal transformations, the geometric mean is just the arithmetic mean with a log transformation.

How harmonic mean is different from arithmetic mean?

What is the relation between arithmetic mean geometric mean and harmonic mean?

The relation between AM GM HM can be represented by the formula AM × HM = GM2. Here the product of the arithmetic mean(AM) and harmonic mean(HM) is equal to the square of the geometric mean(GM).

What is harmonic mean in machine learning?

The harmonic mean is calculated as the number of values N divided by the sum of the reciprocal of the values (1 over each value). Harmonic Mean = N / (1/x1 + 1/x2 + … + 1/xN)

What does F1 score tell you?

Definition: F1 score is defined as the harmonic mean between precision and recall. It is used as a statistical measure to rate performance. In other words, an F1-score (from 0 to 9, 0 being lowest and 9 being the highest) is a mean of an individual’s performance, based on two factors i.e. precision and recall.

Why geometric mean is used?

The geometric mean is used in finance to calculate average growth rates and is referred to as the compounded annual growth rate. Consider a stock that grows by 10% in year one, declines by 20% in year two, and then grows by 30% in year three.

How to calculate harmonic mean?

Since the harmonic mean is the reciprocal of the average of reciprocals, the formula to define the harmonic mean “HM” is given as follows: If x1, x2, x3,…, xnare the individual items up to n terms, then, Harmonic Mean, HM = n / [(1/x1)+(1/x2)+(1/x3)+…+(1/xn)] How to Find a Harmonic Mean?

What is the relationship between geometric mean and harmonic mean?

If G is the geometric mean, H is the harmonic mean, and A is the arithmetic mean, then the relationship between them is given by: [latex]G = \\sqrt{AH}[/latex] Or G2= A.H Weighted Harmonic Mean Calculating weighted harmonic mean is similar to the simple harmonic mean. It is a special case of harmonic mean where all the weights are equal to 1.

What is harmonic mean?

Harmonic Mean (H.M.) Harmonic Mean is defined as the reciprocal of the arithmetic mean of reciprocals of the observations. Let x1, x2., xn be the n observations then the harmonic mean is defined as Example 5.11 A man travels from Jaipur to Agra by a car and takes 4 hours to cover the whole distance.

What is the harmonic mean of ΣΣ f/x?

Σ f/x = 7.879 The formula for weighted harmonic mean is HMw= N / [ (f1/x1) + (f2/x2) + (f3/x3)+ ….(fn/xn) ] HMw= 42 / 7.879 HMw= 5.331 Therefore, the harmonic mean, HMwis 5.331.