Average
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Table of Content:
Average Formulas
Average (Arithmetic Mean)
The average or arithmetic mean of a set of numbers is the sum of the numbers divided by the count of the numbers.
\[
\text{Average} = \frac{\text{Sum of Observations}}{\text{Number of Observations}}
\]
Weighted Average
The weighted average is calculated by multiplying each observation by its respective weight, summing these products, and then dividing by the total sum of the weights.
\[
\text{Weighted Average} = \frac{\sum (w_i \times x_i)}{\sum w_i}
\]
Average Speed
The average speed is the total distance traveled divided by the total time taken.
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
Harmonic Mean
The harmonic mean of a set of numbers is the number of observations divided by the sum of the reciprocals of the observations.
\[
\text{Harmonic Mean} = \frac{n}{\sum \frac{1}{x_i}}
\]
Geometric Mean
The geometric mean of a set of numbers is the nth root of the product of the numbers, where n is the number of observations.
\[
\text{Geometric Mean} = \left( \prod_{i=1}^n x_i \right)^{\frac{1}{n}}
\]