Answered: Todd just got back his exam grades in…

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

Todd just got back his exam grades in three classes. In biology the class mean was 75.80 with a standard deviation of 5.15, Todd got an 84.00. In political science the class mean was 84.00 with a standard deviation of 5.50, Todd got an 84.00. In economics the class mean was 87.50 with a standard deviation of 5.60, Todd got a 84.00.

7. Which class had the lowest average test score?

8. What percentage of the biology class scored higher than Todd?

9. What percentage of the political science class scored lower than Todd?

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 + ...

Expert Solution

Step 1

Consider $X$ as the random obtained score in Biology, Political Science or Economics. For comparing the obtained scores that are observed in three different distributions of scores (i.e., the population distribution), the standardized scores are to be considered. The obtained score in a particular subject is transformed into the standardized score or z-score as: $z = \frac{X - μ}{σ}$

Where, $μ = mean of the distribution of scores σ = standard deviation of the distribution of scores$