Answered: a) Between what two values would you…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1.) The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.4 years. Assume the distribution of the actresses’ ages is approximately unimodal and symmetric.

a) Between what two values would you expect to find about 95% of the lead actresses ages, based on the Empirical Rule?

b) In 2012, popular actress Reese Witherspoon was 36-years-old. What is the z-score for Reese Witherspoon’s age?

c) Would it be unusual for a 36-year-old actress to be in a top-grossing film of 2012?

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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