Answered: Museum membership A museum offers…

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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Museum membership A museum offers several levels
of membership, as shown in the table.a) Find the mean and standard deviation of the donations.
b) During their annual membership drive, they hope to
sign up 50 new members each day. Would you expect
the distribution of the donations for a day to follow a
Normal model? Explain.
c) Consider the mean donation of the 50 new members
each day. Describe the sampling model for these
means (shape, center, and spread).

Member
Category
Amount of
Donation ($)
Percent of
Members
Individual 50 41
Family 100 37
Sponsor 250 14
Patron 500 7
Benefactor 1000 1

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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