Use the following raw scores to answer the questions below.29 21 19 29 20 28 28 29 32 29 15 19 = _____%tile Find the Mean and Standard Deviation of the scores in Excel.mean = Standard Deviation = Convert the first three raw scores in the list on the previous page (29, 21, & 19) to z-scores. 29 = ___________ 21 = ____________ 19 = _____________ You administer a psychological test that has a normal distribution in the population. You know the Mean = 100 and the Standard Deviation = 15. Order the following (a-e) from smallest to largest. Raw Score of 86Z-Score of 1.5Percentile Rank of 98%Score that is 0.5 Standard Deviations below the MeanT-score of 80 _________ _________ _________ _________ _________ Eleanor scores 690 on the SAT math test. The normal distribution of SAT math scores has a mean of 500 and standard deviation of 100. Gerald takes the American College Testing (ACT) Mathematics test and scores 24. ACT scores also follow a normal distribution with a mean of 18 and standard deviation of 6. Find the standardized scores (z-scores) for both students. Assuming that both tests measure the same ability, who has the higher score? Eleanor z-score _________ Gerald z-score _________ Higher scorer is ___________________

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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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Use the following raw scores to answer the questions below.

29 21 19 29 20 28 28 29 32 29 15

19 = _____%tile

Find the Mean and Standard Deviation of the scores in Excel.

mean = Standard Deviation =

Convert the first three raw scores in the list on the previous page (29, 21, & 19) to z-scores.

29 = ___________ 21 = ____________ 19 = _____________

You administer a psychological test that has a normal distribution in the population. You know the Mean = 100 and the Standard Deviation = 15. Order the following (a-e) from smallest to largest.

Raw Score of 86
Z-Score of 1.5
Percentile Rank of 98%
Score that is 0.5 Standard Deviations below the Mean
T-score of 80

_________ _________ _________ _________ _________

Eleanor scores 690 on the SAT math test. The normal distribution of SAT math scores has a mean of 500 and standard deviation of 100. Gerald takes the American College Testing (ACT) Mathematics test and scores 24. ACT scores also follow a normal distribution with a mean of 18 and standard deviation of 6. Find the standardized scores (z-scores) for both students. Assuming that both tests measure the same ability, who has the higher score?

Eleanor z-score _________ Gerald z-score _________

Higher scorer is ___________________

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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