Answered: A standardized test for graduate school…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

A standardized test for graduate school admission has a mean score of

147 with a standard deviation of 11 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 49 at a time. Both organizations publish the mean scores of all their classes.

A mean score of 158 is ______ SD above the mean for the smaller organization, and _______ SD above the mean for the larger organization.

Both organizations advertise that if any class has an average score below 139, they'll pay for everyone to retake the test. Which organization is at greater risk to have to pay?

A mean score of 139 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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