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

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.6: Functions Defined By Tables And Graphs

Problem 8WE

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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
a) Find the Average (arithmetic mean) percentage price adjustment from
2014 to 2019
b) Find the Geometric Mean for the same period
c) 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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