Question

What is the importance of arithmetic mean and geometric mean?

Answer 1

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SOLUTION:--

the geometric mean was introduced to compute the HDI. Poor performance in any dimension is directly reflected in the geometric mean. That is to say, a low achievement in one dimension is not anymore linearly compensated for by high achievement in another dimension. The geometric mean reduces the level of substitutability between dimensions and at the same time ensures that a 1 percent decline in index of, say, life expectancy has the same impact on the HDI as a 1 percent decline in education or income index. Thus, as a basis for comparisons of achievements, this method is also more respectful of the intrinsic differences across the dimensions than a simple average

Answer 2

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The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean ...
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In mathematics, 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 (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of nnumbers, i.e., for a set of numbers x1, x2, ..., xn,