In This Video We Will Discuss the Harmonic Mean in Measures of central tendency and CA Foundation Statistics Chapter - 15 All Problems With Solutions Have Benn Discussed By Chandan Poddar Sir For CA Foundation Grooming Education.
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In this Video:
harmonic mean and geometric mean,
relationship between arithmetic mean and geometric mean,
harmonic mean,
introduction to harmonic mean,
geometric mean and harmonic mean,
how to find harmonic mean by group data,
harmonic mean formula,
concept of harmonic mean by chandan poddar,
application of arithmetic mean geometric mean and harmonic mean,
harmonic mean properties,
properties of harmonic mean by chandan poddar
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 Basics of a Harmonic Mean
The harmonic mean helps to find multiplicative or divisor relationships between fractions without worrying about common denominators. Harmonic means are often used in averaging things like rates (e.g., the average travel speed given a duration of several trips).
The weighted harmonic mean is used in finance to average multiples like the price-earnings ratio because it gives equal weight to each data point. Using a weighted arithmetic mean to average these ratios would give greater weight to high data points than low data points because price-earnings ratios aren't price-normalized while the earnings are equalized.
The harmonic mean is the weighted harmonic mean, where the weights are equal to 1. The weighted harmonic mean of x1, x2, x3 with the corresponding weights w1, w2, w3 is given as:
Harmonic Mean Versus Arithmetic Mean and Geometric Mean
Other ways to calculate averages include the simple arithmetic mean and the geometric mean. An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers. If you were asked to find the class (arithmetic) average of test scores, you would simply add up all the test scores of the students, and then divide that sum by the number of students. For example, if five students took an exam and their scores were 60%, 70%, 80%, 90%, and 100%, the arithmetic class average would be 80%.
The geometric mean is the average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. It is technically defined as "the nth root product of n numbers." The geometric mean must be used when working with percentages, which are derived from values, while the standard arithmetic mean works with the values themselves.
The harmonic mean is best used for fractions such as rates or multiples.
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24 сен 2024
