Answered: standardized algebra test in different…

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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Question

Kaitlyn and Allison took a standardized algebra test in different states. Kaitlyn takes the test for Virginia and scores a 458. Allison takes the test for North Carolina and scores a 185. Suppose the mean and standard deviation for the algebra scores for Virginia are 405 and 30, respectively, and the mean and standard deviation for the algebra scores for North Carolina are 152 and 20, respectively. Which student did better on her algebra test?

Kaitlyn and Allison did equally well since their scores are both above the mean.

Kaitlyn did better since her z-score is higher than Allison’s z-score.

Allison did better since her z-score is higher than Kaitlyn’s z-score.

Allison did better since her z-score is closer to the mean than Kaitlyn’s z-score.

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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