12. Measures of variability match-upThere are multiple ways to refer to or describe a variance or a standard deviation of either a population or a sample. Likewise, each measure has multiple appropriate equations or symbols. The first table consists of alternative ways of referring to each of these measures. The second table consists of equations or symbols for each of these measures.Alternative Description a. Mean squared deviation from the population mean b. Average squared distance from the sample mean c. Square root of the average squared distance from μ d. Standard distance from M Equation or Symbol1.SS/N2.√(∑(X – M)² / (n – 1))3.σ4.SS / (n – 1) For each of the following four measures, select one appropriate description from the first table (lettered) and one appropriate equation or symbol from the second table (numbered). Each answer will be used only once.MeasureAlternative DescriptionEquation or SymbolPopulation standard deviation ? ?Population variance? ?Sample standard deviation ? ?Sample variance ? ?

Relation between variance and standard deviation : In this problem we are to match the type of…

Answered: There are multiple ways to refer to or…

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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12. Measures of variability match-up

There are multiple ways to refer to or describe a variance or a standard deviation of either a population or a sample. Likewise, each measure has multiple appropriate equations or symbols. The first table consists of alternative ways of referring to each of these measures. The second table consists of equations or symbols for each of these measures.

Alternative Description

	a. Mean squared deviation from the population mean
	b. Average squared distance from the sample mean
	c. Square root of the average squared distance from μ
	d. Standard distance from M

Equation or Symbol

1.	SS/N
2.	√(∑(X – M)² / (n – 1))
3.	σ
4.	SS / (n – 1)

For each of the following four measures, select one appropriate description from the first table (lettered) and one appropriate equation or symbol from the second table (numbered). Each answer will be used only once.

Measure	Alternative Description	Equation or Symbol
Population standard deviation	?	?
Population variance	?	?
Sample standard deviation	?	?
Sample variance	?	?

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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