Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions? Why is it useful to compare different distributions? For the following set of scores, fill in the cells. The mean is 74.13 and the standard deviation is 9.98. Raw scoreZ score68.0??–1.682.0??1.869.0??–0.585.0??1.772.0? Questions 3a through 3d are based on a distribution of scores with and the standard deviation = 6.38. Draw a small picture to help you see what is required. What is the probability of a score falling between a raw score of 70 and 80?What is the probability of a score falling above a raw score of 80?What is the probability of a score falling between a raw score of 81 and 83?What is the probability of a score falling below a raw score of 63?

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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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Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions? Why is it useful to compare different distributions?

For the following set of scores, fill in the cells.

The mean is 74.13 and the standard deviation is 9.98.

Raw score	Z score
68.0	?
?	–1.6
82.0	?
?	1.8
69.0	?
?	–0.5
85.0	?
?	1.7
72.0	?

Questions 3a through 3d are based on a distribution of scores with and the standard deviation = 6.38. Draw a small picture to help you see what is required.

What is the probability of a score falling between a raw score of 70 and 80?
What is the probability of a score falling above a raw score of 80?
What is the probability of a score falling between a raw score of 81 and 83?
What is the probability of a score falling below a raw score of 63?

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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