Answered: For the periods 2014 to 2019, ESKOM’s…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.4: The Pythagorean Theorem

Problem 4E: Use theorem 5.4.3 to form a proportion in which TS is a geometric mean. Hint: TVSTSR Exercises 1-6

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Question

For the periods 2014 to 2019, ESKOM’s electricity percentage price adjustments are given in the
following table:
2014/15 2015/16 2016/17 2017/18 2018/19
7.05% 31.70% 8.18% 1.62% 2.82%
Table 1: Average percentage price adjustments

b) Find the Geometric Mean for the same period
Use your answer in a) and b) above to comment on the differences between the two
means. What is the effect of outliers on both the two means?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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