***For any true/false if the statement is false explain why.Standardized observations are always positive. TRUE FALSEThe terms proportion, probability, and area are used interchangeably when working with density curves such as the standard normal curve. TRUE FALSEThe mean for the distribution of a z-score is always zero. TRUE FALSE 1. Standardized observations are always positive. TRUE FALSE2. The terms proportion, probability, and area are used interchangeably when working with densitycurves such as the standard normal curve. TRUE FALSE3. The mean for the distribution of a z-score is always zero. TRUE FALSE

Answered: Standardized observations are always…

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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***For any true/false if the statement is false explain why.

Standardized observations are always positive. TRUE FALSE
The terms proportion, probability, and area are used interchangeably when working with density curves such as the standard normal curve. TRUE FALSE
The mean for the distribution of a z-score is always zero. TRUE FALSE

1. Standardized observations are always positive. TRUE FALSE
2. The terms proportion, probability, and area are used interchangeably when working with density
curves such as the standard normal curve. TRUE FALSE
3. The mean for the distribution of a z-score is always zero. TRUE FALSE

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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Step 1

1) Standardized observations are always positive.

False

Standardized value/observation is also called a z-score. It is a measures which tells how many standard deviations away, a data value is, from the mean. It is given by the formula:

$z = \frac{X - μ}{σ}$

where, $X$ : Raw score

$μ$ : Mean

$σ$ : Standard deviation.

Raw scores are standardized using the above formula and the value we obtain is called a standardized score or observation. It also takes negative values.

For example, a negative standardized value (-2) means that the score is two standard deviation below the mean.

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