Answered: a standard deviation of 9.8, and all…

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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Lauren and Chelsea began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Lauren took a test in Math and earned a 75, and Chelsea took a test in Social Studies and earned a 70. Use the fact that all the students' test grades in the Math class had a mean of 76.4 and a standard deviation of 9.8, and all the students' test grades in Social Studies had a mean of 63.4 and a standard deviation of 9.6 to answer the following questions.

a) Calculate the z-score for Lauren's test grade.
z=z=

b) Calculate the z-score for Chelsea's test grade.
z=z=

c) Which person did relatively better?

Lauren
Chelsea
They did equally well.

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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