Answered: A standardized test for graduate school…

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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A standardized test for graduate school admission has a mean score of 141 with a standard deviation of

10 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 4

students at a time. A larger organization teaches classes of 25 at a time. Both organizations publish the mean scores of all their classes.

If either organization has a graduating class with a mean score of

151,

they'll take out a full-page ad in the local school paper to advertise. Which organization is more likely to have that success? Explain.

A mean score of 151 is ______ SD above the mean for the smaller organization, and _____ SD above the mean for the larger organization.

c) Both organizations advertise that if any class has an average score below

136,

they'll pay for everyone to retake the test. Which organization is at greater risk to have to pay?

A mean score of 136 is ____ SD below the mean for the smaller organization, and ____ SD below the mean for the larger organization

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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