Different types of Mean and their Business Uses-By Riddhi Solanki Group 5 ,Roll no.32.

Different types of Mean and their Business uses

ARITHMETIC MEAN:
 In statistics, the arithmetic mean or simply the mean or average is the sum of a collection of numbers divided by the number of numbers in the collection. The collection is often a set of results of an experiment, or a set of results from a survey. For example, the Arithmetic mean of the following numbers: 9, 3,7,3,8,10,2 is 9+3+7+3+8+10+2 =42/7=6 is the Arithmetic mean. While the arithmetic mean is often used to report central tendencies, it is greatly influenced by outliers (values that are very much larger or smaller than most of the values).
 BUSINESS USE:
 It is frequently used in all the aspects of life. It possesses many mathematical properties and due to this it is of immense utility in further statistical analysis. In economic analysis arithmetic mean is used extensively to calculate average production, average wage, average cost, per capital income exports, imports, consumption, prices, etc. When different items of a series have different relative importance, then weighted arithmetic mean is used. Also, the arithmetic mean is used frequently in fields such as economics, sociology, and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.
 WEIGHTED AVERAGE MEAN: 
The weighted mean is similar to an arithmetic mean, where instead of each of the data points contributing equally to the final average, some data points contribute more than others. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. Given two school classes, one with 20 students, and one with 30 students, the grades in each class on a test were: Morning class = 62, 67, 71, 74, 76, 77, 78, 79, 79, 80, 80, 81, 81, 82, 83, 84, 86, 89, 93, 98 Afternoon class = 81, 82, 83, 84, 85, 86, 87, 87, 88, 88, 89, 89, 89, 90, 90, 90, 90, 91, 91, 91, 92, 92, 93, 93, 94, 95, 96, 97, 98, 99 The straight average for the morning class is 80 and the straight average of the afternoon class is 90. The straight average of 80 and 90 is 85, the mean of the two class means. However, this does not account for the difference in number of students in each class (20 versus 30); hence the value of 85 does not reflect the average student grade (independent of class). The average student grade can be obtained by averaging all the grades, without regard to classes (add all the grades up and divide by the total number of students): Or, this can be accomplished by weighting the class means by the number of students in each class (using a weighted mean of the class means): Thus, the weighted mean makes it possible to find the average student grade in the case where only the class means and the number of students in each class are available.
 GEOMETRIC MEAN: 
The geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values It is defined as the nth root (where n is the count of numbers) of the product of the numbers. For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is .
BUSINESS USE: 
Use of Geometric mean is important in a series having items of wide dispersion. It is used in the construction of index number. The averages of proportions, percentages and compound rates are computed by geometric mean. The growth of population is measured in it as population increases in geometric progression.
HARMONIC MEAN:
 In mathematics, the harmonic mean (sometimes called the sub contrary mean) is one of several kinds of mean and hence one of several kinds of average.. It is the special case (M−1) of the power mean. As it tends strongly toward the least elements of the list, it may (compared to the arithmetic mean) mitigate the influence of large outliers and increase the influence of small values.
 BUSINESS USE:
Harmonic mean is applied in the problems where small items must get more relative importance than the large ones. It is useful in cases where time, speed, values given in quantities, rate and prices are involved. But in practice, it has little applicability.
TRIMMED MEAN: 
The trimmed mean looks to reduce the effects of outliers on the calculated average. This method is best suited for data with large, erratic deviations or extremely skewed distributions. A trimmed mean is stated as a mean trimmed by X%, where X is the sum of the percentage of observations removed from both the upper and lower bounds. For example, a figure skating competition produces the following scores: 6.0, 8.1, 8.3, 9.1, and 9.9. A mean trimmed 40% would equal 8.5 ((8.1+8.3+9.1)/3), which is larger than the arithmetic mean of 8.28. To trim the mean by 40%, we remove the lowest 20% and highest 20% of values, eliminating the scores of 6.0 and 9.1. As shown by this example, trimming the mean can reduce the effects of outlier bias in a sample.
SOURCE:
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