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Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter10: Exponential And Logarithmic Functions

Section10.3: Evaluate And Graph Logarithmic Functions

Problem 10.53TI: In 1906, San Francisco experienced an intense earthquake with a magnitude of 7.8 on the Richter...

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Question

An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure " distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and number of days until deaths began in each later group:

Distance xx	2	5	4	4	4	6
Days yy	4	21	29	40	47	49

Use a calculator or software to find the following values.

(a) Find the mean and standard deviation of xx.

MEAN:
STANDARD DEVIATION:

(b) Find the mean and standard deviation of yy.

MEAN:
STANDARD DEVIATION:

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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